A294503 Inverse binomial transform of A026007.

1, 0, 1, 1, -3, 10, -23, 48, -92, 171, -321, 626, -1265, 2576, -5099, 9478, -15925, 22617, -21816, -8506, 121659, -436121, 1204710, -2962759, 6860591, -15427559, 34323613, -76269455, 169591278, -376162414, 827819644, -1798045927, 3839392935, -8041078328

Offset

0,5

Links

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

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A026007(k).

G.f.: (1/(1 + x))*Product_{k>=1} (1 + x^k/(1 + x)^k)^k. - Ilya Gutkovskiy, Aug 20 2018

Mathematica

nmax = 40; s = CoefficientList[Series[Product[(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}]

Crossrefs

Cf. A026007, A294501, A294502, A294505.

Sequence in context: A293350 A256525 A192973 * A080204 A115982 A167243

Adjacent sequences: A294500 A294501 A294502 * A294504 A294505 A294506

Keyword

sign

Author

Vaclav Kotesovec, Nov 01 2017

Status

approved