OFFSET
0,10
COMMENTS
a(n) is also the number of forests of 8 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
LINKS
FORMULA
G.f.: x^8/((1-8x)(1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)(1-15x)(1-16x)).
E.g.f.: exp(8*x)*((exp(x)-1)^8)/8!.
MAPLE
a:= proc(k::nonnegint) local M; M:= Matrix(k+1, (i, j)-> if (i=j-1) then 1 elif j=1 then [seq(-1* coeff(product(1-t*x, t=k..2*k), x, u), u=1..k+1)][i] else 0 fi); p-> (M^p)[1, k+1] end(8); seq(a(n), n=0..27);
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 12 2008
STATUS
approved