diff --git a/arb.h b/arb.h
index ced4c9b5..6d6536dc 100644
--- a/arb.h
+++ b/arb.h
@@ -616,6 +616,8 @@ void arb_zeta_ui(arb_t z, ulong n, long prec);
 void arb_hurwitz_zeta(arb_t z, const arb_t s, const arb_t a, long prec);
 void arb_bernoulli_ui(arb_t z, ulong n, long prec);
 
+void arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, long len, long prec);
+
 void arb_rising_ui_bs(arb_t y, const arb_t x, ulong n, long prec);
 void arb_rising_ui_rs(arb_t y, const arb_t x, ulong n, ulong m, long prec);
 void arb_rising_ui_rec(arb_t y, const arb_t x, ulong n, long prec);
diff --git a/arb/power_sum_vec.c b/arb/power_sum_vec.c
new file mode 100644
index 00000000..632caaea
--- /dev/null
+++ b/arb/power_sum_vec.c
@@ -0,0 +1,68 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2015 Fredrik Johansson
+
+******************************************************************************/
+
+#include "arb.h"
+#include "bernoulli.h"
+#include "arb_poly.h"
+
+/* todo: don't use exact bernoulli numbers for large len */
+/* todo: output exact integers when precise enough */
+void
+arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, long len, long prec)
+{
+    arb_ptr t, u, v;
+    long k;
+
+    if (len < 1)
+        return;
+
+    t = _arb_vec_init(len + 1);
+    u = _arb_vec_init(len + 1);
+    v = _arb_vec_init(len + 1);
+
+    /* exp(ax), exp(bx) */
+    arb_set(t + 1, a);
+    arb_set(u + 1, b);
+    _arb_poly_exp_series(t, t, 2, len + 1, prec);
+    _arb_poly_exp_series(u, u, 2, len + 1, prec);
+    _arb_vec_sub(t, u, t, len + 1, prec);
+
+    /* x/(exp(x)-1) */
+    BERNOULLI_ENSURE_CACHED(len + 1);
+    for (k = 0; k <= len; k++)
+        arb_set_fmpq(u + k, bernoulli_cache + k, prec);
+    _arb_poly_borel_transform(u, u, len + 1, prec);
+
+    _arb_poly_mullow(v, t, len + 1, u, len + 1, len + 1, prec);
+    _arb_poly_inv_borel_transform(v, v, len + 1, prec);
+
+    for (k = 0; k < len; k++)
+        arb_div_ui(res + k, v + k + 1, k + 1, prec);
+
+    _arb_vec_clear(t, len + 1);
+    _arb_vec_clear(u, len + 1);
+    _arb_vec_clear(v, len + 1);
+}
+
diff --git a/arb/test/t-power_sum_vec.c b/arb/test/t-power_sum_vec.c
new file mode 100644
index 00000000..67a38624
--- /dev/null
+++ b/arb/test/t-power_sum_vec.c
@@ -0,0 +1,91 @@
+/*=============================================================================
+
+    This file is part of ARB.
+
+    ARB is free software; you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation; either version 2 of the License, or
+    (at your option) any later version.
+
+    ARB is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with ARB; if not, write to the Free Software
+    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
+
+=============================================================================*/
+/******************************************************************************
+
+    Copyright (C) 2015 Fredrik Johansson
+
+******************************************************************************/
+
+#include "arb.h"
+
+int main()
+{
+    long iter;
+    flint_rand_t state;
+
+    printf("power_sum_vec....");
+    fflush(stdout);
+
+    flint_randinit(state);
+
+    for (iter = 0; iter < 1000; iter++)
+    {
+        arb_t a, b, s, t;
+        arb_ptr res;
+        long aa, bb, k, n, len;
+        long prec;
+
+        len = n_randint(state, 30);
+        prec = 2 + n_randint(state, 500);
+        aa = n_randint(state, 50) - 50;
+        bb = aa + n_randint(state, 50);
+
+        arb_init(a);
+        arb_init(b);
+        arb_init(s);
+        arb_init(t);
+        res = _arb_vec_init(len);
+
+        arb_set_si(a, aa);
+        arb_set_si(b, bb);
+        arb_power_sum_vec(res, a, b, len, prec);
+
+        for (n = 0; n < len; n++)
+        {
+            arb_zero(s);
+            for (k = aa; k < bb; k++)
+            {
+                arb_set_si(t, k);
+                arb_pow_ui(t, t, n, prec);
+                arb_add(s, s, t, prec);
+            }
+
+            if (!arb_overlaps(res + n, s))
+            {
+                printf("FAIL: overlap\n\n");
+                printf("a = %ld, b = %ld, n = %ld\n\n", aa, bb, n);
+                printf("res = "); arb_printd(res + n, 30); printf("\n\n");
+                printf("s = "); arb_printd(s, 30); printf("\n\n");
+                abort();
+            }
+        }
+
+        arb_clear(a);
+        arb_clear(b);
+        arb_clear(s);
+        arb_clear(t);
+        _arb_vec_clear(res, len);
+    }
+
+    flint_randclear(state);
+    flint_cleanup();
+    printf("PASS\n");
+    return EXIT_SUCCESS;
+}
diff --git a/doc/source/arb.rst b/doc/source/arb.rst
index e8b28138..3e346067 100644
--- a/doc/source/arb.rst
+++ b/doc/source/arb.rst
@@ -1162,6 +1162,23 @@ Bernoulli numbers
     enough and `n` large enough for the Euler product to converge
     rapidly (otherwise this function will effectively hang).
 
+.. function:: void arb_power_sum_vec(arb_ptr res, const arb_t a, const arb_t b, long len, long prec)
+
+    For *n* from 0 to *len* - 1, sets entry *n* in the output vector *res* to
+
+    .. math ::
+
+        S_n(a,b) = \frac{1}{n+1}\left(B_{n+1}(b) - B_{n+1}(a)\right)
+
+    where `B_n(x)` is a Bernoulli polynomial. If *a* and *b* are integers
+    and `b \ge a`, this is equivalent to
+
+    .. math ::
+
+        S_n(a,b) = \sum_{k=a}^{b-1} k^n.
+
+    The computation uses the generating function for Bernoulli polynomials.
+
 Polylogarithms
 -------------------------------------------------------------------------------