A294505 Inverse binomial transform of A156616.

1, 1, 3, 3, 3, 7, -3, 13, -5, -7, 49, -97, 93, 155, -997, 2893, -5989, 9007, -7121, -10805, 63305, -169375, 321137, -418503, 152653, 1142657, -4565939, 11378145, -21893565, 32887315, -33140953, -1985517, 113177979, -348817177, 734074637, -1210600023

Offset: 0

Author

Vaclav Kotesovec, Nov 01 2017

Keywords

• sign

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..3000

Crossrefs

Cf. A156616, A294501, A294503, A294504.

Programs

Mathematica

nmax = 40; s = CoefficientList[Series[Product[((1+x^k)/(1-x^k))^k, {k, 1, nmax}], {x, 0, nmax}], x]; Table[Sum[(-1)^(n-k) * Binomial[n, k] * s[[k+1]], {k, 0, n}], {n, 0, nmax}]

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A156616(k).

G.f.: (1/(1 + x))*exp(Sum_{k>=1} (sigma_2(2*k) - sigma_2(k))*x^k/(2*k*(1 + x)^k)). - Ilya Gutkovskiy, Oct 15 2018