A362391 E.g.f. satisfies A(x) = exp(x + x^3/2 * A(x)).

1, 1, 1, 4, 25, 121, 751, 7351, 73417, 749449, 9477181, 136883341, 2041250641, 33289802833, 608025141907, 11815916748091, 242532915013201, 5369303859003601, 126896359555326745, 3153096762426186553, 82705881733348530241, 2293511922269658189121

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..427

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

Formula

E.g.f.: exp(x - LambertW(-x^3/2 * exp(x))) = -2 * LambertW(-x^3/2 * exp(x))/x^3.

a(n) = n! * Sum_{k=0..floor(n/3)} (1/2)^k * (k+1)^(n-2*k-1) / (k! * (n-3*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^3/2*exp(x)))))

Crossrefs

Column k=3 of A362378.

Cf. A362380, A362479.

Sequence in context: A069639 A013582 A260373 * A175733 A240479 A317949

Adjacent sequences: A362388 A362389 A362390 * A362392 A362393 A362394

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2023

Status

approved