A145458 Exponential transform of C(n,8) = A000581.

1, 0, 0, 0, 0, 0, 0, 0, 1, 9, 45, 165, 495, 1287, 3003, 6435, 19305, 243100, 3981978, 49959702, 498967170, 4190469570, 30728937690, 201931408074, 1213163827326, 6849350570700, 39615797628550, 296414654550300, 3418235092302030

Offset: 0

Author

Alois P. Heinz, Oct 10 2008

Keywords

• nonn

Comments

a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 8 balls are seen at the top.

a(n) is also the number of forests of labeled rooted trees of height at most 1, with n labels, where each root contains 8 labels.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

8th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *binomial(j,8) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..35);

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Exp[x] x^8/8!],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Feb 05 2020 *)

Formula

E.g.f.: exp(exp(x)*x^8/8!).