A145454 Exponential transform of binomial(n,4) = A000332.

1, 0, 0, 0, 1, 5, 15, 35, 105, 756, 6510, 46530, 283470, 1667380, 11457446, 99776040, 969295145, 9298091180, 86154691680, 804769174536, 8052676029420, 88489327173660, 1038440150703340, 12501684521410700, 151866259113256611

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 4 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 4 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

4th column of A145460, A143398.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n-1, j-1) *binomial(j,4) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..30);

Mathematica

Table[Sum[BellY[n, k, Binomial[Range[n], 4]], {k, 0, n}], {n, 0, 25}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Formula

E.g.f.: exp(exp(x)*x^4/4!).