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

0,2

Comments

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)

Links

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

Mathematica

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

Prog

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

Crossrefs

For denominators see A157867, and also A288872.

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

Sequence in context: A156363 A221929 A283432 * A221852 A363196 A025230

Adjacent sequences: A157863 A157864 A157865 * A157867 A157868 A157869

Keyword

sign,frac

Author

N. J. A. Sloane, Nov 08 2009

Status

approved