A368321 Expansion of e.g.f. exp(4*x) / (3 - 2*exp(x)).

1, 6, 42, 354, 3642, 45426, 673962, 11641314, 229708122, 5098836306, 125752998282, 3411596337474, 100968384710202, 3237242806231986, 111776324007217002, 4135115023742364834, 163175176006352025882, 6841471526492783720466, 303716608443703306594122

Offset: 0

Author

Seiichi Manyama, Dec 21 2023

Keywords

• nonn

Crossrefs

Cf. A004123, A201339, A368319, A368320.

Programs

PARI

b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=4, t=2) = my(u=1+1/t); u^m*b(n, t)-(1/t)*sum(j=0, m-1, u^j*(m-1-j)^n);

Formula

a(n) = 4^n + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).

a(n) = (81/16)*A004123(n+1) - (1/2)*(3^n + (3/2)*2^n + 9/4 + (27/8)*0^n).