A145456 Exponential transform of C(n,6) = A000579.

1, 0, 0, 0, 0, 0, 1, 7, 28, 84, 210, 462, 1386, 13728, 171171, 1686685, 13461448, 91495768, 551777772, 3142726692, 19787406360, 172188951144, 1999835600301, 24655331721867, 285725747201356, 3034790658153100, 29876851476502030

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 6 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 6 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

6th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *binomial(j,6) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..30);

Mathematica

With[{nn=30},CoefficientList[Series[Exp[Exp[x] x^6/6!],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 14 2018 *)

Formula

E.g.f.: exp(exp(x)*x^6/6!).