A367972 Expansion of e.g.f. exp(exp(2*x) - 1)/(1 - x).
1, 3, 14, 82, 568, 4504, 40016, 392368, 4198784, 48616320, 604921600, 8043848960, 113785080832, 1705669278720, 27007064393728, 450422751508480, 7893590619881472, 145052304752934912, 2789743827826573312, 56063169473909817344
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, ((j-1)!+2^j)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} ((k-1)! + 2^k) * binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..n} 2^k * Bell(k)/k!, where Bell() is A000110.