A362336 a(n) = n! * Sum_{k=0..floor(n/5)} (n/120)^k /(k! * (n-5*k)!).

1, 1, 1, 1, 1, 6, 37, 148, 449, 1135, 15121, 172789, 1207009, 6106816, 24748725, 510855346, 8524169473, 84981641837, 602009065729, 3357322881625, 93871272204481, 2059974308136466, 26683062726210661, 243032907824598816, 1725747644222610625

Offset: 0

Author

Seiichi Manyama, Apr 16 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..484
• Eric Weisstein's World of Mathematics, Lambert W-Function.

Crossrefs

Cf. A362173, A362317.

Cf. A275423, A362319, A362323.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((-24*lambertw(-x^5/24))^(1/5))/(1+lambertw(-x^5/24))))

Formula

a(n) = n! * [x^n] exp(x + n*x^5/120).

E.g.f.: exp( ( -24*LambertW(-x^5/24) )^(1/5) ) / (1 + LambertW(-x^5/24)).