A392772 a(n) = Sum_{k=0..n} Stirling2(3*n,k).

1, 1, 32, 3281, 700075, 255514355, 142508723651, 112871151708404, 120582710957928740, 167261566992144276462, 292533334396074979037085, 630259347221767611416981753, 1641445572311721534326982547311, 5087593060551511875179001983091509, 18521515421264267606291278809759249311

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

a(n) ~ 3^(3*n) * n^(3*n) / (sqrt(1 + LambertW(3*n)) * LambertW(3*n)^(3*n) * exp(3*n + 1 - 3*n/LambertW(3*n))).

Mathematica

Table[Sum[StirlingS2[3*n, k], {k, 0, n}], {n, 0, 20}]

Prog

(PARI) a(n) = sum(k=0, n, stirling(3*n, k, 2)); \\ Michel Marcus, Jan 22 2026

Crossrefs

Cf. A000110, A008277, A359355, A392771, A143815.

Sequence in context: A016793 A215045 A219343 * A123802 A264057 A221659

Adjacent sequences: A392769 A392770 A392771 * A392773 A392774 A392775

Keyword

nonn

Author

Vaclav Kotesovec, Jan 22 2026

Status

approved