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%I #9 Sep 15 2017 07:51:55
%S 1,-2,-2,-6,-22,-130,-870,-6578,-56270,-533346,-5551534,-63053074,
%T -776254350,-10302652946,-146717718254,-2232271391058,-36147843303406,
%U -620859957094930,-11275285124686446,-215901942195987986,-4347742535086701038,-91860773988102875922
%N Expansion of Product_{k>=1} ((1 - k!*x^k)/(1 + k!*x^k)).
%F Convolution of A292279 and A292280.
%F Convolution inverse of A292318.
%F 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
%t 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 *)
%Y Cf. A292279, A292280, A292318.
%K sign
%O 0,2
%A _Seiichi Manyama_, Sep 14 2017
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