A372346 a(n) = Sum_{j=0..n} p(n - j, j) where p(n, x) = Sum_{k=0..n} k! * Stirling2(n, k) * x^k. Row sums of A344499.

1, 1, 2, 6, 27, 175, 1532, 17276, 243093, 4165261, 85133686, 2039546786, 56447550543, 1783865468187, 63766726231792, 2558290237404920, 114418196763735113, 5670168958036693977, 309630356618418661738, 18536683645526372648446, 1211038603734731649106307, 85983731724631359047504967

Offset: 0

Author

Peter Luschny, Apr 28 2024

Keywords

• nonn

Crossrefs

Cf. A344499, A131689, A094422.

Programs

Maple

p := n -> local k; add(k!*Stirling2(n, k)*x^k, k = 0..n):
a := n -> local j; add(subs(x = j, p(n - j)),  j = 0..n):
seq(a(n), n = 0..21);

Formula

a(n) = A094422(n - 1) + 1.