A143402 Expansion of x^k/Product_{t=k..2k} (1-tx) for k=7.

0, 0, 0, 0, 0, 0, 0, 1, 84, 3990, 141120, 4138827, 106469748, 2484848080, 53791898160, 1096912870053, 21307466872692, 397605494092170, 7173885616672320, 125794299357058879, 2152559266567924116, 36065247772657686660, 593280221500152370800

Offset: 0

Author

Alois P. Heinz, Aug 12 2008

Keywords

• nonn

Comments

a(n) is also the number of forests of 7 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..300
• Index entries for sequences related to rooted trees

Crossrefs

7th 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(7): seq(a(n), n=0..30);

Formula

G.f.: x^7/((1-7x)(1-8x)(1-9x)(1-10x)(1-11x)(1-12x)(1-13x)(1-14x)).

E.g.f.: exp(7*x)*((exp(x)-1)^7)/7!.