OFFSET
0,7
COMMENTS
a(n) is the number of ways of placing n labeled balls into indistinguishable boxes, where in each filled box 5 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 5 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^5/5!).
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(binomial(n-1, j-1) *binomial(j, 5) *a(n-j), j=1..n))
end:
seq(a(n), n=0..30);
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Exp[Exp[x]*x^5/5!], {x, 0, nmax}], x]] (* G. C. Greubel, Nov 21 2017 *)
PROG
(PARI) x='x+O('x^30); Vec(serlaplace(exp(exp(x)*x^5/5!))) \\ G. C. Greubel, Nov 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 10 2008
STATUS
approved