%I #16 Oct 04 2017 18:39:08

%S 1,1,0,5,-13,75,-465,3509,-29492,276310,-2854776,32242512,-395295109,

%T 5230184477,-74303722489,1128399929626,-18245417102767,

%U 313000130900207,-5678742973964699,108649510570970878,-2186444702147475131,46169315317847827548

%N G.f.: Product_{i>0} 1/(Sum_{j>=0} (-1)^j*j!*x^(j*i)).

%H Seiichi Manyama, <a href="/A293259/b293259.txt">Table of n, a(n) for n = 0..449</a>

%F Convolution inverse of A293236.

%F a(n) ~ -(-1)^n * n! * (1 - 2/n - 7/n^3 - 39/n^4 - 272/n^5 - 2457/n^6 - 26443/n^7 - 324675/n^8 - 4453439/n^9 - 67360840/n^10), for coefficients see A293265. - _Vaclav Kotesovec_, Oct 04 2017

%t nmax = 30; CoefficientList[Series[Product[1/Sum[(-1)^j*j!*x^(j*k), {j, 0, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Oct 04 2017 *)

%Y Cf. A293236, A293251.

%K sign

%O 0,4

%A _Seiichi Manyama_, Oct 04 2017