A368320 Expansion of e.g.f. exp(3*x) / (3 - 2*exp(x)).
1, 5, 31, 245, 2455, 30365, 449551, 7761605, 153140935, 3399230765, 83835351871, 2274397617365, 67312256650615, 2158161871352765, 74517549339738991, 2756743349166359525, 108783450670915699495, 4560981017661898860365, 202477738962469000202911
Offset: 0
Keywords
Programs
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PARI
b(n, t) = sum(k=0, n, t^k*k!*stirling(n, k, 2)); a(n, m=3, 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) = 3^n + 2 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (27/8)*A004123(n+1) - (1/2)*(2^n + 3/2 + (9/4)*0^n).