OFFSET
0,6
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
FORMULA
E.g.f.: exp(exp(x)*x^4/4!).
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2008
STATUS
approved