A157883 Numerator of Bernoulli(n, 2/5).

1, -1, -11, 3, 91, -43, -12347, 1183, 62851, -54423, -39448591, 3799763, 27287144401, -375591203, -34562009741, 49954996743, 89299092717107, -8604866798383, -135379643536733633, 1863607913992123, 2694379428323830241, -495661415843787963, -1648224141847799919403

Offset

0,3

Comments

From Wolfdieter Lang, Jul 05 2017: (Start)

a(n) gives also the numerators of the generalized Bernoulli numbers B[5,2](n) = 5^n*Bernoulli(n, 2/5) with the Bernoulli polynomials B(n, x) = Bernoulli(n, x) from A196838/A196839 or A053382/A053383. For the denominators see A288872(n) = A157867(n)/5^n. See a comment under A157866 for B[d,a](n).

(-1)^n*a(n) gives the numerators of the generalized Bernoulli numbers B[5,3](n); the denominators are A288872(n).

(End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..250

Mathematica

Table[Numerator[BernoulliB[n, 2/5]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)

Prog

(PARI) a(n) = numerator(subst(bernpol(n, x), x, 2/5)); \\ Michel Marcus, Jul 06 2017
(Python)
from sympy import bernoulli, Integer
def a(n): return bernoulli(n, Integer(2)/5).numerator()
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 06 2017

Crossrefs

For denominators see A157867.

Cf. A288872.

Sequence in context: A204845 A260597 A147555 * A038317 A157781 A069869

Adjacent sequences: A157880 A157881 A157882 * A157884 A157885 A157886

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 08 2009

Status

approved