A293251 G.f.: Product_{i>0} 1/(Sum_{j>=0} j!*x^(j*i)).

1, -1, -2, -3, -13, -65, -447, -3351, -28544, -269270, -2795872, -31689198, -389581679, -5165672203, -73512910689, -1117937393138, -18096787251877, -310743077434399, -5642249024063207, -108023468997424550, -2175086628366359447, -45952007357795606912

Offset: 0

Author

Seiichi Manyama, Oct 04 2017

Keywords

• sign

Links

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

Crossrefs

Cf. A161779, A293259.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[1/Sum[j!*x^(j*k), {j, 0, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 04 2017 *)

Formula

Convolution inverse of A161779.

a(n) ~ -n! * (1 - 2/n - 2/n^2 - 5/n^3 - 29/n^4 - 232/n^5 - 2231/n^6 - 24745/n^7 - 308917/n^8 - 4279945/n^9 - 65179552/n^10), for coefficients see A293264. - Vaclav Kotesovec, Oct 04 2017