A363529 E.g.f. satisfies A(x) = exp(x * (1 + x * A(x)^4)).

1, 1, 3, 31, 409, 7361, 170251, 4732351, 154694961, 5814634753, 246946119571, 11698927124831, 611660759515081, 34984757221103041, 2173041881789331099, 145669007565799127551, 10482025117382045382241, 805892200757926620144641

Offset

0,3

Links

Table of n, a(n) for n=0..17.

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

Formula

E.g.f.: exp( x - LambertW(-4*x^2*exp(4*x))/4 ).

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

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-4*x^2*exp(4*x))/4)))

Crossrefs

Cf. A125500, A143768, A363354.

Sequence in context: A136596 A186207 A014178 * A123818 A087591 A061053

Adjacent sequences: A363526 A363527 A363528 * A363530 A363531 A363532

Keyword

nonn

Author

Seiichi Manyama, Aug 17 2023

Status

approved