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A292280 Expansion of Product_{k>=1} (1 - k!*x^k). 2
1, -1, -2, -4, -18, -84, -564, -3984, -33504, -307728, -3156192, -35254080, -429350400, -5641133760, -79720588800, -1204747741440, -19400679325440, -331599765565440, -5996988417784320, -114408970262922240, -2296442484579686400, -48379417944213196800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A077365, A265950.

Sequence in context: A318230 A075836 A295370 * A120664 A095816 A020101

Adjacent sequences:  A292277 A292278 A292279 * A292281 A292282 A292283

KEYWORD

sign

AUTHOR

Seiichi Manyama, Sep 13 2017

STATUS

approved

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)