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%I #11 Dec 21 2023 10:24:07
%S 1,6,42,354,3642,45426,673962,11641314,229708122,5098836306,
%T 125752998282,3411596337474,100968384710202,3237242806231986,
%U 111776324007217002,4135115023742364834,163175176006352025882,6841471526492783720466,303716608443703306594122
%N Expansion of e.g.f. exp(4*x) / (3 - 2*exp(x)).
%F a(n) = 4^n + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).
%F a(n) = (81/16)*A004123(n+1) - (1/2)*(3^n + (3/2)*2^n + 9/4 + (27/8)*0^n).
%o (PARI) b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2));
%o 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);
%Y Cf. A004123, A201339, A368319, A368320.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 21 2023
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