A363010 a(n) = n! * [x^n] 1/(1 - f^n(x)), where f(x) = exp(x) - 1.

1, 1, 4, 36, 594, 15775, 618838, 33757864, 2448904188, 228290728635, 26617527649365, 3797508644987398, 651082351708066303, 132130157056046918808, 31333332827346731906130, 8587011712002719806274022, 2693586800519167315881703732, 958983405298849163873718493941

Offset: 0

Author

Seiichi Manyama, May 12 2023

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..246

Crossrefs

Main diagonal of A363007.

Main diagonal of A153278 (for n>=1).

Cf. A139383, A261280, A346802, A351433.

Programs

Maple

b:= proc(n, t, m) option remember; `if`(n=0, `if`(t<2, m!,
      b(m, t-1, 0)), m*b(n-1, t, m)+b(n-1, t, m+1))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..20);  # Alois P. Heinz, May 12 2023

Formula

a(n) = T(n,n), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = n!.