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
Programs
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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
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Mathematica
Table[Sum[Binomial[n, k]*(k+1)*BernoulliB[k], {k, 0, n}], {n, 0, 60}] // Denominator (* Vaclav Kotesovec, Oct 05 2016 *) -
Maxima
makelist(denom(sum((binomial(n, i)*(i+1)*bern(i)), i, 0, n)), n, 0, 20); /* Vladimir Kruchinin, Oct 05 2016 */
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PARI
a(n) = denominator(sum(i=0, n, binomial(n,i)*(i+1)*bernfrac(i))); \\ Michel Marcus, Oct 05 2016
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
Comments