A145459 Exponential transform of C(n,9) = A000582.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 72930, 1016158, 18643560, 258952330, 2845739820, 26177047270, 209411148144, 1495786618975, 9722602868550, 58373582056075, 329869586346300, 1861266055353705

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 9 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 9 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

9th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *binomial(j,9) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..35);

Formula

E.g.f.: exp(exp(x)*x^9/9!).