A140219 Denominator of the coefficient [x^1] of the Bernoulli twin number polynomial C(n,x).

1, 1, 2, 2, 6, 6, 6, 6, 10, 10, 6, 6, 210, 210, 2, 2, 30, 30, 42, 42, 110, 110, 6, 6, 546, 546, 2, 2, 30, 30, 462, 462, 170, 170, 6, 6, 51870, 51870, 2, 2, 330, 330, 42, 42, 46, 46, 6, 6, 6630, 6630, 22, 22, 30, 30, 798, 798, 290

Offset

0,3

Comments

See A140351 for the main part of the documentation.

Links

Table of n, a(n) for n=0..56.

Formula

a(n) = denominator(Sum_{i=0..n} binomial(n,i)*(i+1)*bern(i)). - Vladimir Kruchinin, Oct 05 2016

a(n) = A006955(floor(n/2)). - Georg Fischer, Nov 29 2022

Maple

C := proc(n, x) if n = 0 then 1; else add(binomial(n-1, j-1)* bernoulli(j, x), j=1..n) ; expand(%) ; end if ; end proc:
A140219 := proc(n) coeff(C(n, x), x, 1) ; denom(%) ; end proc:
seq(A140219(n), n=1..80) ; # R. J. Mathar, Sep 22 2011

Mathematica

Table[Sum[Binomial[n, k]*(k+1)*BernoulliB[k], {k, 0, n}], {n, 0, 60}] // Denominator (* Vaclav Kotesovec, Oct 05 2016 *)

Prog

(Maxima) makelist(denom(sum((binomial(n, i)*(i+1)*bern(i)), i, 0, n)), n, 0, 20); /* Vladimir Kruchinin, Oct 05 2016 */
(PARI) a(n) = denominator(sum(i=0, n, binomial(n, i)*(i+1)*bernfrac(i))); \\ Michel Marcus, Oct 05 2016

Crossrefs

Cf. A002427, A006955, A048594, A140351 (numerators).

Sequence in context: A196872 A319865 A350657 * A259225 A300951 A077081

Adjacent sequences: A140216 A140217 A140218 * A140220 A140221 A140222

Keyword

nonn,frac

Author

Paul Curtz, Jun 23 2008

Status

approved