A368236 Expansion of e.g.f. 1/(exp(-x) - 2*x).
1, 3, 17, 145, 1649, 23441, 399865, 7957881, 180997857, 4631289697, 131670338921, 4117813225769, 140486274499345, 5192341564319313, 206669931188282073, 8813624820931402201, 400922608851086766017, 19377398675442025382081, 991639882680576890150089
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, 2^(n-k)*(n-k+1)^k/k!);
Formula
a(0) = 1; a(n) = 2*n*a(n-1) + Sum_{k=1..n} (-1)^(k-1) * binomial(n,k) * a(n-k).
a(n) = n! * Sum_{k=0..n} 2^(n-k) * (n-k+1)^k / k!.
a(n) ~ n! / (2 * LambertW(1/2)^(n+1) * (LambertW(1/2) + 1)). - Vaclav Kotesovec, Dec 29 2023