A115023 a(n) = numerator of the sum s(n) of the reciprocals of the Bernoulli numbers B(2k), k=0..n.

1, 7, -23, 19, -11, 11, -6049, -21613, -90508571, -3900532722347, -682342247955237967, -582977855082068353785701, -137796593884898105670153879336641, -1178587648547585802037207041523952332253, -3998688919354698660438533512261373544028557044041

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..41

Mathematica

Accumulate[1/BernoulliB[2*Range[0, 20]]]//Numerator (* Harvey P. Dale, Jun 01 2025 *)

Prog

(PARI)
partial_sums(v) = {my(w=vector(#v)); w[1]=v[1]; for(i=2, #v, w[i]=w[i-1]+v[i]); w}
a115023(size) = {p=partial_sums(vector(size, k, k--; 1/bernfrac(2*k))); vector(size, k, numerator(p[k]))}
a115023(20) \\ Colin Barker, May 19 2015
(Python)
from sympy import bernoulli
def A115023(n): return (sum(1/bernoulli(2*k) for k in range(n+1))).numerator # David Radcliffe, Aug 01 2025

Crossrefs

Sequence in context: A175483 A121815 A025172 * A009228 A249438 A349230

Adjacent sequences: A115020 A115021 A115022 * A115024 A115025 A115026

Keyword

sign,frac

Author

Pasquale Cutolo (p.cutolo(AT)inwind.it), Feb 24 2006

Extensions

a(0) = 1 inserted by N. J. A. Sloane, Jun 02 2025 at the suggestion of Harvey P. Dale.

Status

approved