login
A230342
Number of permutations of [2n+2] in which the longest increasing run has length n+2.
3
1, 6, 67, 1024, 19710, 456720, 12372360, 383685120, 13406178240, 521194867200, 22318001798400, 1043827513344000, 52949040240096000, 2895555891900672000, 169823181579891840000, 10633812541718446080000, 708077586604965857280000, 49962245750984840232960000
OFFSET
0,2
COMMENTS
Also the number of ascending runs of length n+2 in the permutations of [2n+2].
LINKS
FORMULA
a(n) = (n^3+6*n^2+12*n+11)*(2*n+2)!/(n+4)! for n>0, a(0) = 1.
a(n) = A008304(2*n+2,n+2) = A122843(2*n+2,n+2).
MAPLE
a:= proc(n) option remember; `if`(n<2, 1+5*n, 2*(n+1)*(2*n+1)*
(n^3+6*n^2+12*n+11)*a(n-1)/((n+4)*(n^3+3*n^2+3*n+4)))
end:
seq(a(n), n=0..25);
CROSSREFS
A diagonal of A008304, A122843.
Sequence in context: A231598 A073562 A354320 * A239301 A121958 A177555
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2013
STATUS
approved