A373871 a(n) = Sum_{k=1..n} k! * k^(n-3) * Stirling2(n,k).

0, 1, 2, 13, 233, 8311, 495437, 44495263, 5619239453, 949995402271, 207228784973597, 56681221280785663, 19000392210559326173, 7661410911700580500831, 3658694812581483750630557, 2042247041839449013948374463, 1317554928647608644852032652893

Offset: 0

Author

Seiichi Manyama, Jun 20 2024

Keywords

• nonn

Crossrefs

Cf. A373869, A373870, A373872.

Cf. A122399, A244585, A373873.

Programs

PARI

a(n) = sum(k=1, n, k!*k^(n-3)*stirling(n, k, 2));

Formula

E.g.f.: Sum_{k>=1} (exp(k*x) - 1)^k / k^3.