A293259 G.f.: Product_{i>0} 1/(Sum_{j>=0} (-1)^j*j!*x^(j*i)).

1, 1, 0, 5, -13, 75, -465, 3509, -29492, 276310, -2854776, 32242512, -395295109, 5230184477, -74303722489, 1128399929626, -18245417102767, 313000130900207, -5678742973964699, 108649510570970878, -2186444702147475131, 46169315317847827548

Offset: 0

Author

Seiichi Manyama, Oct 04 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A293236, A293251.

Programs

Mathematica

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 *)

Formula

Convolution inverse of A293236.

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