|
|
A143402
|
|
Expansion of x^k/Product_{t=k..2k} (1-tx) for k=7.
|
|
2
|
|
|
0, 0, 0, 0, 0, 0, 0, 1, 84, 3990, 141120, 4138827, 106469748, 2484848080, 53791898160, 1096912870053, 21307466872692, 397605494092170, 7173885616672320, 125794299357058879, 2152559266567924116, 36065247772657686660, 593280221500152370800
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,9
|
|
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
|
|
|
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!.
|
|
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);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|