A292308 - OEIS

%I #12 Sep 14 2017 09:30:57

%S 1,-1,1,-4,21,-96,520,-3795,32053,-284368,2763876,-30648465,373339824,

%T -4833294389,67167087793,-1009753574739,16215467043493,

%U -275361718915824,4947532173402532,-94054153646919213,1882793796608183356,-39528099512321898363

%N E.g.f.: 1/Product_{k>=1} (1 + x^k/k!).

%F a(n) = (-1)^n * A076901(n).

%F a(n) ~ c * (-1)^n * n!, where c = Product_{k>=2} (1 + (-1)^k/k!) = 0.77351587386... - _Vaclav Kotesovec_, Sep 14 2017

%t nmax = 20; Table[SeriesCoefficient[Product[1/(1 + x^k/k!), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 14 2017 *)

%Y Cf. A005651, A007837, A076901.

%K sign

%O 0,4

%A _Seiichi Manyama_, Sep 14 2017