A216912 a(n) = denominator(B°(2*n))/4 where the B°(n) are Zagier's modified Bernoulli numbers.

6, 20, 315, 280, 66, 3003, 78, 9520, 305235, 20900, 138, 19734, 6, 7540, 15575175, 590240, 6, 107666559, 222, 11996600, 50536395, 19780, 282, 31534932, 66, 1060, 48532365, 738920, 354, 83912718435, 366, 1180480, 485415, 1340, 60918, 3667092237666, 438, 740

Offset

1,1

Comments

Sequence given for a(1)-a(15) in Note 6.2, p. 13 of Dixit and others.

Links

Seiichi Manyama, Table of n, a(n) for n = 1..500

M. W. Coffey, V. de Angelis, A. Dixit, V. H. Moll, et al., The Zagier polynomials. Part II: Arithmetic properties of coefficients, arXiv:1303.6590 [math.NT], 2013.

A. Dixit, V. H. Moll, Ch. Vignat, The Zagier modification of Bernoulli numbers and a polynomial extension. Part I, arXiv:1209.4110v1 [math.NT], Sep 18, 2012.

Maple

A216912 := n -> denom(add(binomial(2*n+r, 2*r)*bernoulli(r)/(2*n+r), r=0..2*n))/4;
seq(A216912(i), i=1..38); # Peter Luschny, Sep 20 2012

Mathematica

a[n_] := Denominator[Sum[Binomial[2n+r, 2r]*(BernoulliB[r]/(2n+r)), {r, 0, 2n}]]/4;
Array[a, 38] (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *)

Prog

(PARI) a(n) = denominator(sum(k=0, 2*n, binomial(2*n+k, 2*k)*bernfrac(k)/(2*n+k)))/4; \\ Michel Marcus, Jul 14 2018

Crossrefs

Cf. A216922, A216923.

Sequence in context: A267903 A330825 A280039 * A175671 A222741 A338427

Adjacent sequences: A216909 A216910 A216911 * A216913 A216914 A216915

Keyword

nonn

Author

Jonathan Vos Post, Sep 20 2012

Extensions

a(16)-a(38) from Peter Luschny, Sep 20 2012

Status

approved