A288872 -id:A288872 - cp's OEIS frontend

A157866 Numerator of Bernoulli(n, 1/5).

1, -3, 1, 6, -29, -74, 4537, 1946, -23789, -88434, 15034541, 6154786, -10417027559, -607884394, 13199705071, 80834386026, -34108052679853, -13923204233954, 51709981061257363, 3015393801263666, -1029159167703800359, -801997872697905114, 629565265428734672873

Offset: 0

N. J. A. Sloane, Nov 08 2009

From Wolfdieter Lang, Jul 05 2017: (Start)
a(n) gives also the numerators of the generalized Bernoulli numbers B[5,1](n) = 5^n*B(n, 1/5) 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.
(-1)^n*a(n) gives the numerators of the generalized Bernoulli numbers B[5,4](n). The denominators are also A288872(n).
The generalized Bernoulli numbers B[d,a](n), for d >= 1, a >= 0, with gcd(d, a) = 1 are defined in terms of generalized Stirling2 numbers by B[d,a](n) = Sum_{k=0..n} ((-1)^k / (k+1))*S2[d,a](n, k)*k!, n >= 0. See A285061 for more details.
(End)

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

For denominators see A157867, and also A288872.

Cf. A053382/A053383, A196838/A196839, A285061.

Table[Numerator[BernoulliB[n, 1/5]], {n, 0, 50}] (* Vincenzo Librandi, Mar 16 2014 *)

a(n)=numerator(subst(bernpol(n, x), x, 1/5)); \\ Michel Marcus, Jul 06 2017

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

Original entry on oeis.org

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

N. J. A. Sloane, Nov 08 2009

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)

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

For denominators see A157867.

Cf. A288872.

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

a(n) = numerator(subst(bernpol(n, x), x, 2/5)); \\ Michel Marcus, Jul 06 2017

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

cp's OEIS Frontend

A157866 Numerator of Bernoulli(n, 1/5).

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