A371041 E.g.f. satisfies A(x) = exp(x^2*A(x)^3) / (1-x).

1, 1, 4, 30, 348, 5460, 108480, 2609040, 73713360, 2393087760, 87791891040, 3591843726240, 162157925160000, 8007919490450880, 429418816003457280, 24849579630222547200, 1543505958412498080000, 102430107277414595078400, 7232759636684706937612800

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

E.g.f.: (LambertW( -3*x^2/(1-x)^3 ) / (-3*x^2))^(1/3).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(-3*x^2/(1-x)^3)/(-3*x^2))^(1/3)))
(PARI) a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*binomial(n+k, n-2*k)/k!);

Crossrefs

Cf. A360609, A370876.

Sequence in context: A209440 A052316 A089918 * A132622 A218296 A118792

Adjacent sequences: A371038 A371039 A371040 * A371042 A371043 A371044

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2024

Status

approved