login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A157866 Numerator of Bernoulli(n, 1/5). 4
1, -3, 1, 6, -29, -74, 4537, 1946, -23789, -88434, 15034541, 6154786, -10417027559, -607884394, 13199705071, 80834386026, -34108052679853, -13923204233954, 51709981061257363, 3015393801263666, -1029159167703800359, -801997872697905114, 629565265428734672873 (list; graph; refs; listen; history; text; internal format)
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 A025230 A152456

Adjacent sequences:  A157863 A157864 A157865 * A157867 A157868 A157869

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Nov 08 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)