A368322 Expansion of e.g.f. exp(2*x) / (4 - 3*exp(x)).
1, 5, 37, 389, 5413, 94085, 1962277, 47746949, 1327769893, 41538664325, 1443908686117, 55210237509509, 2302968844974373, 104068337416767365, 5064468256286449957, 264065894676248072069, 14686540175450593986853, 867871886679723760867205
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=2, 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);
Formula
a(n) = 2^n + 3 * Sum_{k=1..n} binomial(n,k) * a(n-k).
a(n) = (16/9)*A032033(n) - (1/3)*(1 + (4/3)*0^n).