A362523 a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) / (k! * (n-3*k)!).

1, 1, 1, 7, 25, 61, 1201, 7771, 30577, 1058905, 9904321, 53722351, 2708688841, 33126146197, 228967340785, 15262865820931, 230517745701601, 1936173471789361, 161021598306402817, 2894434429492525015, 28614958982310290041

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)) = -LambertW(-x^3)/x^3 * exp(x).

Prog

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

Crossrefs

Cf. A088957, A362522.

Cf. A089464, A362348.

Sequence in context: A118396 A330044 A193375 * A362348 A185787 A299273

Adjacent sequences: A362520 A362521 A362522 * A362524 A362525 A362526

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 23 2023

Status

approved