A143401 Expansion of x^k/Product_{t=k..2k} (1-tx) for k=6.

0, 0, 0, 0, 0, 0, 1, 63, 2282, 62370, 1428987, 28979181, 537306484, 9302333040, 152587968533, 2396472657579, 36320866824606, 534421447961310, 7670116319449039, 107781064078390857, 1487396442778796648, 20208696810429799980, 270879169288278532905

Offset: 0

Author

Alois P. Heinz, Aug 12 2008

Keywords

• nonn

Comments

a(n) is also the number of forests of 6 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

6th 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(6); seq(a(n), n=0..27);

Formula

G.f.: x^6/((1-6x)(1-7x)(1-8x)(1-9x)(1-10x)(1-11x)(1-12x)).

E.g.f.: exp(6*x)*((exp(x)-1)^6)/6!.