A367845 Expansion of e.g.f. 1/(1 - x + log(1 - 2*x)).
1, 3, 22, 250, 3816, 72968, 1675568, 44901456, 1375306368, 47392683648, 1814635323648, 76430014409472, 3511792144942080, 174806087920727040, 9370642040786049024, 538202280800536799232, 32972397141008692445184, 2146270648672407967137792
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^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^k * (k-1)! * binomial(n,k) * a(n-k).
a(n) ~ n! * 2^(n+1) / ((1/LambertW(1/(2*exp(1/2))) - 1 - 2*LambertW(1/(2*exp(1/2)))) * (1 - 2*LambertW(1/(2*exp(1/2))))^n). - Vaclav Kotesovec, Dec 02 2023