A364987 E.g.f. satisfies A(x) = 1 + x*exp(x)*A(x)^4.

1, 1, 10, 183, 5140, 196005, 9468486, 554425963, 38171336680, 3022130473065, 270537702834250, 27021535857472431, 2979254055371578524, 359411244032212931533, 47093111659782104431438, 6660135357832421444841555, 1011181346455643980818939856

Offset

0,3

Links

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

Formula

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*k+1,k)/( (4*k+1)*(n-k)! ) = n! * Sum_{k=0..n} k^(n-k) * A002293(k)/(n-k)!.

a(n) ~ 2*sqrt(1 + LambertW(27/256)) * n^(n-1) / (3^(3/2) * exp(n) * LambertW(27/256)^n). - Vaclav Kotesovec, Nov 11 2024

Prog

(PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*k, k)/((3*k+1)*(n-k)!));

Crossrefs

Cf. A006153, A295238, A364983.

Cf. A002293, A349331.

Sequence in context: A240405 A304936 A239764 * A179521 A211102 A121973

Adjacent sequences: A364984 A364985 A364986 * A364988 A364989 A364990

Keyword

nonn

Author

Seiichi Manyama, Aug 15 2023

Status

approved