A368017 Expansion of e.g.f. exp(exp(x) - exp(3*x)).

1, -2, -4, 14, 144, 286, -5080, -61058, -186144, 4016958, 73395928, 468915102, -4728823088, -167453193314, -2051810224568, -406640603074, 533831885402048, 11987797433266302, 110763307665075640, -1459040819952150178, -80503810962755821904

Offset: 0

Author

Seiichi Manyama, Dec 08 2023

Keywords

• sign

Crossrefs

Cf. A355378.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (1-3^j)*binomial(i-1, j-1)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (1 - 3^k) * binomial(n-1,k-1) * a(n-k).