OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 18 2024
STATUS
approved