login
A230348
Number of permutations of [2n+8] in which the longest increasing run has length n+8.
3
1, 18, 349, 7672, 192240, 5454144, 173606040, 6143195520, 239656253760, 10231052832000, 474832908950400, 23819880180096000, 1284985968634368000, 74207855717259264000, 4569213387521502720000, 298885288012537901875200, 20702796608070625112064000
OFFSET
0,2
COMMENTS
Also the number of ascending runs of length n+8 in the permutations of [2n+8].
LINKS
FORMULA
a(n) = (n^3+18*n^2+90*n+89)*(2*n+8)!/(n+10)! for n>0, a(0) = 1.
a(n) = A008304(2*n+8,n+8) = A122843(2*n+8,n+8).
MAPLE
a:= proc(n) option remember; `if`(n<2, 1+17*n, 2*(n+4)*(2*n+7)*
(n^3+18*n^2+90*n+89)*a(n-1)/((n+10)*(n^3+15*n^2+57*n+16)))
end:
seq(a(n), n=0..25);
CROSSREFS
A diagonal of A008304, A122843.
Sequence in context: A158590 A143168 A127585 * A366684 A182609 A320764
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2013
STATUS
approved