A292279 Expansion of 1/Product_{k>=1} (1 + k!*x^k).

1, -1, -1, -5, -15, -93, -551, -4129, -33607, -312929, -3179343, -35602881, -432201743, -5678740945, -80142780751, -1210609725905, -19481112885231, -332836223507793, -6016678424942063, -114746996449871761, -2302527084416470255, -48495552665272893329

Offset: 0

Author

Seiichi Manyama, Sep 13 2017

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A077365, A265950.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Product[1/(1 + k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 13 2017 *)

PARI

{a(n) = polcoeff(1/prod(k=1, n, 1+k!*x^k+x*O(x^n)), n)}

Formula

Convolution inverse of A265950.

a(n) ~ -n! * (1 - 1/n - 1/n^2 - 6/n^3 - 31/n^4 - 219/n^5 - 1932/n^6 - 19945/n^7 - 234837/n^8 - 3104108/n^9 - 45495817/n^10). - Vaclav Kotesovec, Sep 14 2017

G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^k*(j!)^k*x^(j*k)/k). - Ilya Gutkovskiy, Jun 18 2018