A392747 a(n) = Sum_{k=0..n} Stirling2(n+3*k,2*k).

1, 7, 1716, 1331453, 2151119533, 5938064541933, 25001581180419574, 149146087541448025113, 1197001151269888963598710, 12438152383638540661198890270, 162463054412281434919873901126151, 2605489905334911696096494773053052893, 50333834408520079001698097784322059257809

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..140

Formula

a(n) ~ 2^(6*n-1) * n^(2*n - 1/2) / (sqrt(Pi*(1-w)) * exp(2*n) * w^(2*n) * (2-w)^(2*n)), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.406375739959959907676958...

Mathematica

Table[Sum[StirlingS2[n+3*k, 2*k], {k, 0, n}], {n, 0, 12}]

Prog

(Magma) [&+[StirlingSecond(n+3*k, 2*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Feb 20 2026

Crossrefs

Cf. A229286, A392726, A392734.

Cf. A226775.

Sequence in context: A308441 A220989 A284705 * A203012 A203697 A001424

Adjacent sequences: A392744 A392745 A392746 * A392748 A392749 A392750

Keyword

nonn

Author

Vaclav Kotesovec, Jan 21 2026

Status

approved