A363478 E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x)^3).

1, 1, 9, 142, 3481, 115476, 4849639, 246746662, 14756605329, 1014635520424, 78869009859751, 6839463570354306, 654661145565724345, 68559809182824171148, 7797979656027302949159, 957275139494698134599806, 126152927575064012671549729

Offset

0,3

Links

Table of n, a(n) for n=0..16.

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

Formula

E.g.f.: exp( -LambertW(-3*x * (1+x))/3 ).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x*(1+x))/3)))

Crossrefs

Cf. A362771, A362773.

Sequence in context: A371365 A083084 A187402 * A303147 A317354 A050787

Adjacent sequences: A363475 A363476 A363477 * A363479 A363480 A363481

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved