A292319 Expansion of Product_{k>=1} ((1 - k!*x^k)/(1 + k!*x^k)).
1, -2, -2, -6, -22, -130, -870, -6578, -56270, -533346, -5551534, -63053074, -776254350, -10302652946, -146717718254, -2232271391058, -36147843303406, -620859957094930, -11275285124686446, -215901942195987986, -4347742535086701038, -91860773988102875922
Offset: 0
Keywords
Programs
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Mathematica
nmax = 25; CoefficientList[Series[Product[(1 - k!*x^k)/(1 + k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 15 2017 *)
Formula
Convolution inverse of A292318.
a(n) ~ -2 * n! * (1 - 2/n - 2/n^2 - 8/n^3 - 42/n^4 - 306/n^5 - 2812/n^6 - 30246/n^7 - 368710/n^8 - 5015300/n^9 - 75279670/n^10). - Vaclav Kotesovec, Sep 15 2017