A043303 Numerator of B(4n+2)/(2n+1) where B(m) are the Bernoulli numbers.

1, 1, 1, 1, 43867, 77683, 657931, 1723168255201, 151628697551, 154210205991661, 1520097643918070802691, 25932657025822267968607, 19802288209643185928499101, 29149963634884862421418123812691

Offset

0,5

Comments

Note that numerator of B(2n)/n is odd so B(2n)/(2n), B(2n)/(4n), etc. have the same numerators. - Michael Somos, Feb 01 2004

References

Bruce Berndt, Ramanujan's Notebooks Part II, Springer-Verlag; see Infinite series, p. 262.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..156

Formula

B(4n+2)/(8n+4) = sum_{k>=1} k^(4n+1)/(exp(2Pi*k)-1)).

Maple

seq(numer(bernoulli(4*n+2)/(2*n+1)), n=0..30); # Robert Israel, Sep 18 2016

Mathematica

Table[BernoulliB[4n+2]/(2n+1), {n, 0, 20}]//Numerator (* Harvey P. Dale, Aug 13 2018 *)

Prog

(PARI) a(n)=if(n<0, 0, numerator(bernfrac(4*n+2)/(2*n+1)))

Crossrefs

Cf. A043304. a(n)=A001067(2n+1).

Sequence in context: A206517 A279892 A037147 * A233790 A359127 A223457

Adjacent sequences: A043300 A043301 A043302 * A043304 A043305 A043306

Keyword

easy,frac,nonn

Author

Benoit Cloitre, Apr 04 2002

Status

approved