A143403 Expansion of x^k/Product_{t=k..2k} (1-tx) for k=8.

0, 0, 0, 0, 0, 0, 0, 0, 1, 108, 6510, 289080, 10550067, 335170836, 9597839680, 253489991040, 6275077781973, 147318890173884, 3309320153700210, 71623038281001480, 1501654449863348119, 30633757929391948452, 610246760750629071300, 11906371167306982146000

Offset: 0

Author

Alois P. Heinz, Aug 12 2008

Keywords

• nonn

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

• Alois P. Heinz, Table of n, a(n) for n = 0..250
• Index entries for sequences related to rooted trees

Crossrefs

8th column of A143395.

Programs

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);

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!.