A292280 Expansion of Product_{k>=1} (1 - k!*x^k).

1, -1, -2, -4, -18, -84, -564, -3984, -33504, -307728, -3156192, -35254080, -429350400, -5641133760, -79720588800, -1204747741440, -19400679325440, -331599765565440, -5996988417784320, -114408970262922240, -2296442484579686400, -48379417944213196800

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 - k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 13 2017 *)

PARI

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

Formula

Convolution inverse of A077365.

a(n) ~ -n! * (1 - 1/n - 2/n^2 - 6/n^3 - 32/n^4 - 222/n^5 - 1916/n^6 - 19650/n^7 - 231200/n^8 - 3058566/n^9 - 44883428/n^10). - Vaclav Kotesovec, Sep 14 2017

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