A371318 E.g.f. satisfies A(x) = exp(x) + x*A(x)^3.

1, 2, 13, 190, 4345, 135346, 5345749, 256004974, 14416470961, 933597699202, 68358972056221, 5584583237569150, 503607231488672425, 49690178089937051122, 5325031693664693833957, 615922452708451717999726, 76479190243720703567763553

Offset

0,2

Links

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

Formula

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

a(n) ~ sqrt(1 + LambertW(8/27)) * 2^n * n^(n-1) / (3 * exp(n) * LambertW(8/27)^(n + 1/2)). - Vaclav Kotesovec, Jun 01 2024

Mathematica

Table[n! Sum[(2 k + 1)^(n - k - 1)*Binomial[3 k, k]/(n - k)!, {k, 0, n}], {n, 0, 20}] (* Wesley Ivan Hurt, May 25 2024 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(n-k-1)*binomial(3*k, k)/(n-k)!);

Crossrefs

Cf. A000522, A194471, A373324.

Sequence in context: A356491 A226865 A062156 * A323209 A239994 A242007

Adjacent sequences: A371315 A371316 A371317 * A371319 A371320 A371321

Keyword

nonn

Author

Seiichi Manyama, Mar 18 2024

Status

approved