A368446 Expansion of e.g.f. exp(-x) / (1 + log(1 - 2*x)).
1, 1, 9, 81, 1025, 16177, 306793, 6791201, 171849153, 4892782241, 154792866953, 5387090968113, 204528939571521, 8412441383512657, 372629008281155177, 17684630326318986881, 895251144144309285505, 48152984520621412552257
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+sum(j=1, i, 2^j*(j-1)!*binomial(i, j)*v[i-j+1])); v;
Formula
a(n) = (-1)^n + Sum_{k=1..n} 2^k * (k-1)! * binomial(n,k) * a(n-k).