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A368324
Expansion of e.g.f. exp(4*x) / (4 - 3*exp(x)).
2
1, 7, 61, 679, 9589, 167167, 3488221, 84882679, 2360477509, 73846507567, 2566948755181, 98151533290279, 4094166835331029, 185010377629273567, 9003499122285420541, 469450479424436219479, 26109404756356597154149, 1542883354097286642881167
OFFSET
0,2
FORMULA
a(n) = 4^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (256/81)*A032033(n) - (1/3)*(3^n + (4/3)*2^n + 16/9 + (64/27)*0^n).
PROG
(PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
a(n, m=4, t=3) = 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