A375993 Expansion of e.g.f. (4 - 3 * exp(x))^(5/3).
1, -5, 5, 35, 165, 1075, 10805, 152035, 2719365, 58547475, 1469512405, 42082036035, 1353220758565, 48264167285875, 1890433757030005, 80656857839376035, 3723074712045197765, 184851684577600696275, 9822823990059902723605, 556226222504163445932035
Offset: 0
Programs
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PARI
a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-5)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..n} (Product_{j=0..k-1} (3*j-5)) * Stirling2(n,k).
a(n) ~ 5 * sqrt(Pi) * 2^(29/6) * n^(n - 13/6) / (9 * Gamma(1/3) * exp(n) * log(4/3)^(n - 5/3)). - Vaclav Kotesovec, Sep 06 2024