A362393 E.g.f. satisfies A(x) = exp(x + x^4 * A(x)).

1, 1, 1, 1, 25, 241, 1441, 6721, 87361, 1729729, 24816961, 270452161, 3705324481, 85344916801, 1992230175937, 38047293910081, 709217112938881, 17385498239168641, 514103858592923521, 14254662916125735553, 366807994235438359681, 10338786602768939575681

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..422

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

Formula

E.g.f.: exp(x - LambertW(-x^4 * exp(x))) = -LambertW(-x^4 * exp(x))/x^4.

a(n) = n! * Sum_{k=0..floor(n/4)} (k+1)^(n-3*k-1) / (k! * (n-4*k)!).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-x^4*exp(x)))))

Crossrefs

Cf. A125500, A362392.

Cf. A362431.

Sequence in context: A278849 A294290 A352304 * A107943 A125388 A126546

Adjacent sequences: A362390 A362391 A362392 * A362394 A362395 A362396

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2023

Status

approved