A382000 - OEIS

%I #14 Mar 22 2025 10:56:42

%S 1,1,14,342,12872,659280,42828912,3375009568,312860626304,

%T 33361836534144,4023352486200320,541461682626399744,

%U 80448618080927609856,13079749459734097573888,2309915877337042992324608,440332184936376095626076160,90117169223076699520606896128

%N E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^5.

%F a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A002294(k)/(n-k)!.

%F a(n) ~ 2^(n-3) * n^(n-1) * sqrt(5*(1 + LambertW(512/3125))) / (exp(n) * LambertW(512/3125)^n). - _Vaclav Kotesovec_, Mar 22 2025

%o (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(5*k+1, k)/((5*k+1)*(n-k)!));

%Y Cf. A336950, A381997, A381998, A381999, A382001.

%Y Cf. A002294, A377526, A381986.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 12 2025