A368015 Expansion of e.g.f. 1/(1 - exp(2*x) + exp(3*x)).

1, -1, -3, 5, 81, 29, -4623, -20035, 415041, 4838909, -46093743, -1309934275, 3230184801, 419574363389, 2065056788337, -154120122603715, -2307971235744639, 59954627542249469, 1959892188447337617, -19474957767402204355, -1658215397958862557279

Offset: 0

Author

Seiichi Manyama, Dec 08 2023

Keywords

• sign

Crossrefs

Cf. A355409.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (2^j-3^j)*binomial(i, j)*v[i-j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=1..n} (2^k - 3^k) * binomial(n,k) * a(n-k).