A380155 Expansion of e.g.f. 1/sqrt(1 - 2*x*exp(2*x)).
1, 1, 7, 63, 785, 12545, 244407, 5619775, 148977313, 4473497601, 150078670055, 5563415292479, 225832882678449, 9962766560986369, 474619650950131351, 24283168467229957695, 1327993894505461755713, 77305844496338607597569, 4772660185400974888323015
Offset: 0
Keywords
Programs
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PARI
a(n) = 2^n*n!*sum(k=0, n, (-1)^k*k^(n-k)*binomial(-1/2, k)/(n-k)!);
Formula
a(n) = 2^n * n! * Sum_{k=0..n} (-1)^k * k^(n-k) * binomial(-1/2,k)/(n-k)!.
a(n) == 1 (mod 2).
a(n) ~ 2^(n + 1/2) * n^n / (sqrt(1 + LambertW(1)) * exp(n) * LambertW(1)^n). - Vaclav Kotesovec, Jan 23 2025