A367973 Expansion of e.g.f. exp(exp(x) - 1)/(1 - 2*x).
1, 3, 14, 89, 727, 7322, 88067, 1233815, 19745180, 355434387, 7108803715, 156394360300, 3753468860797, 97590218025159, 2732526295603774, 81975790251071765, 2623225298514438627, 89189660232355783122
Offset: 0
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, (2^j*(j-1)!+1)*binomial(i-1, j-1)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (2^k * (k-1)! + 1) * binomial(n-1,k-1) * a(n-k).
a(n) = n! * Sum_{k=0..n} 2^(n-k) * Bell(k)/k!, where Bell() is A000110.