A362573 E.g.f. satisfies A(x) = exp(x * A(x)^(x^2/6)).

1, 1, 1, 1, 5, 21, 61, 351, 2521, 13105, 96041, 933021, 7098301, 65348141, 787190405, 7896243811, 88712631281, 1269172794401, 15784837036561, 210688183375705, 3486485630182581, 51674172769168741, 801474314335394701, 15059801657898920231, 258815184609843935305

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..470

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

Formula

E.g.f.: (-6 * LambertW(-x^3/6) / x^3)^(6/x^2) = exp(-6 * LambertW(-x^3/6) / x^2) = exp(x * exp(-LambertW(-x^3/6))).

a(n) = n! * Sum_{k=0..floor(n/3)} ((n-2*k)/6)^k * binomial(n-2*k-1,k)/(n-2*k)!.

E.g.f.: Sum_{k>=0} (k*x^2/6 + 1)^(k-1) * x^k / k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(-lambertw(-x^3/6)))))

Crossrefs

Cf. A000272, A362572.

Cf. A362571.

Sequence in context: A351934 A356328 A147216 * A196631 A357723 A342379

Adjacent sequences: A362570 A362571 A362572 * A362574 A362575 A362576

Keyword

nonn

Author

Seiichi Manyama, Apr 25 2023

Status

approved