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%I #15 Apr 18 2023 08:28:35
%S 1,1,1,1,2,6,16,36,211,1387,6511,23431,225721,2207921,14610597,
%T 71848141,958259121,12403693681,105819536881,659686502257,
%U 11235532306021,180826378073461,1888306425160541,14256573124903341,295428115205647117,5683724892725141901
%N a(n) = n! * Sum_{k=0..floor(n/4)} (k/24)^k / (k! * (n-4*k)!).
%H Seiichi Manyama, <a href="/A362352/b362352.txt">Table of n, a(n) for n = 0..494</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F E.g.f.: exp(x) / (1 + LambertW(-x^4/24)).
%F a(n) ~ (exp(2^(3/4)*3^(1/4)*exp(-1/4)) + (-1)^n/exp(2^(3/4)*3^(1/4)*exp(-1/4)) + 2*cos(2^(3/4)*3^(1/4)*exp(-1/4) - Pi*n/2)) * n^n / (2^(3*n/4 + 1) * 3^(n/4) * exp(3*n/4)). - _Vaclav Kotesovec_, Apr 18 2023
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x)/(1+lambertw(-x^4/24))))
%Y Cf. A362350, A362351.
%Y Cf. A362317.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Apr 17 2023
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