A362319 a(n) = n! * Sum_{k=0..floor(n/5)} (n/5)^k / (k! * (n-5*k)!).

1, 1, 1, 1, 1, 121, 865, 3529, 10753, 27217, 7318081, 96720625, 689990401, 3508289929, 14239793569, 5933573525881, 114415115802625, 1165402803391009, 8298505279241857, 46355961619888993, 26167218073714552321, 663290722580370585625

Offset

0,6

Links

Winston de Greef, Table of n, a(n) for n = 0..434

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

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

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

Prog

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

Crossrefs

Cf. A277614, A362300, A362314.

Sequence in context: A293588 A365969 A203959 * A211472 A223389 A243810

Adjacent sequences: A362316 A362317 A362318 * A362320 A362321 A362322

Keyword

nonn

Author

Seiichi Manyama, Apr 16 2023

Status

approved