A380014 Expansion of e.g.f. 1/sqrt(exp(-2*x) - 2*x).
1, 2, 10, 88, 1084, 17176, 332824, 7623904, 201540112, 6038820640, 202246657696, 7486877795200, 303561658686400, 13378863292503424, 636833910410881408, 32559375816074384896, 1779494669204225605888, 103532173699456380625408, 6388705590982575700625920
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (-2)^k*(2*k+1)^(n-k)*binomial(-1/2, k)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (-2)^k * (2*k+1)^(n-k) * binomial(-1/2,k)/(n-k)!.
a(n) ~ 2^(n + 1/2) * n^n / (sqrt(1 + LambertW(1)) * LambertW(1)^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Jan 23 2025