A367828 E.g.f. A(x) satisfies A(x) = (1 - log(1 - x) * A(2*x)) / (1 - x).
1, 2, 13, 209, 7874, 687194, 138026428, 63273019396, 65547617642192, 151904702763916944, 780028188748068778464, 8799101018162158392857376, 216405047530763040469557821568, 11527355297347542160143184818391680, 1322291382391922104463259686181056293632
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]=i*v[i]+sum(j=1, i, 2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} 2^(n-k) * (k-1)! * binomial(n,k) * a(n-k).