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A368321
Expansion of e.g.f. exp(4*x) / (3 - 2*exp(x)).
2
1, 6, 42, 354, 3642, 45426, 673962, 11641314, 229708122, 5098836306, 125752998282, 3411596337474, 100968384710202, 3237242806231986, 111776324007217002, 4135115023742364834, 163175176006352025882, 6841471526492783720466, 303716608443703306594122
OFFSET
0,2
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).
PROG
(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);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 21 2023
STATUS
approved