|
Search: id:A143400
|
|
|
| A143400 |
|
Expansion of x^k/Prod_{t=k..2k}(1-tx) for k=5. |
|
+0
2
|
|
| 0, 0, 0, 0, 0, 1, 45, 1190, 24150, 416451, 6427575, 91549480, 1227283200, 15695180501, 193333245105, 2310273772170, 26927270656650, 307413790470151, 3449088814306635, 38132767214613260, 416342920938136500
(list; graph; listen)
|
|
|
OFFSET
|
0,7
|
|
|
COMMENT
|
a(n) is also the number of forests of 5 labeled rooted trees of height at most 1 with n labels, where any root may contain >= 1 labels.
|
|
LINKS
|
Index entries for sequences related to rooted trees
|
|
FORMULA
|
G.f.: x^5/((1-5x)(1-6x)(1-7x)(1-8x)(1-9x)(1-10x)).
|
|
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(5); seq (a(n), n=0..27);
|
|
CROSSREFS
|
5th column of A143395.
Sequence in context: A163721 A140346 A049447 this_sequence A004350 A075515 A145151
Adjacent sequences: A143397 A143398 A143399 this_sequence A143401 A143402 A143403
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 12 2008
|
|
|
Search completed in 0.002 seconds
|
