A373539 Expansion of e.g.f. exp(x/(1 + x^3)^(1/3)).
1, 1, 1, 1, -7, -39, -119, 841, 10641, 59473, -393679, -9119439, -77841719, 453247081, 17769103353, 210702481081, -1002688100959, -65813075987679, -1022777654395679, 3554736409105633, 413233827275657241, 8091508938651283321, -16214426267734966039
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n\3, (-1)^k*binomial(n/3-1, k)/(n-3*k)!);
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (-1)^k * binomial(n/3-1,k)/(n-3*k)!.
a(n) == 1 mod 8.