A145457 Exponential transform of C(n,7) = A000580.

1, 0, 0, 0, 0, 0, 0, 1, 8, 36, 120, 330, 792, 1716, 5148, 57915, 835120, 9354488, 84047184, 638567124, 4256855760, 25607297880, 144863655024, 869425029957, 7081044528888, 83816629147900, 1131047706331400, 14634713798592030, 173380501913172840

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 7 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 7 labels.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..556 (terms 0..200 from Alois P. Heinz)
• N. J. A. Sloane, Transforms
• Index entries for sequences related to rooted trees

Crossrefs

7th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *binomial(j,7) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..30);

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n - 1, j - 1] *Binomial[j, 7]* a[n - j], {j, 1, n}]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Formula

E.g.f.: exp(exp(x)*x^7/7!).