A392734 a(n) = Sum_{k=0..n} Stirling2(n+k,k).

1, 1, 8, 106, 2034, 51325, 1607640, 60185328, 2622090774, 130336661775, 7279900110152, 451406774382630, 30769652547034920, 2286911102645633100, 184063553458946253120, 15949042011102816698400, 1480313394342131407456830, 146524412397114081529683235, 15407030789080441728746016528

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

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

Mathematica

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

Prog

(Magma) [&+[ StirlingSecond(n+k, k) : k in [0..n] ] : n in [0..18]]; // Vincenzo Librandi, Jan 23 2026

Crossrefs

Cf. A354978, A392733, A229286.

Cf. A226775.

Sequence in context: A112701 A380258 A395122 * A099695 A236953 A345474

Adjacent sequences: A392731 A392732 A392733 * A392735 A392736 A392737

Keyword

nonn

Author

Vaclav Kotesovec, Jan 21 2026

Status

approved