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A230343
Number of permutations of [2n+3] in which the longest increasing run has length n+3.
3
1, 8, 99, 1602, 32010, 761904, 21064680, 663848640, 23500653120, 923616691200, 39914540709120, 1881558401184000, 96096062174112000, 5286518167746816000, 311689569962010240000, 19608741674518284288000, 1311187373310480906240000, 92868537238628772741120000
OFFSET
0,2
COMMENTS
Also the number of ascending runs of length n+3 in the permutations of [2n+3].
LINKS
FORMULA
a(n) = (n^3+8*n^2+20*n+19)*(2*n+3)!/(n+5)! for n>0, a(0) = 1.
a(n) = A008304(2*n+3,n+3) = A122843(2*n+3,n+3).
MAPLE
a:= proc(n) option remember; `if`(n<2, 1+7*n, 2*(2*n+3)*(n+1)*
(n^3+8*n^2+20*n+19)*a(n-1)/((n+5)*(n^3+5*n^2+7*n+6)))
end:
seq(a(n), n=0..25);
CROSSREFS
A diagonal of A008304, A122843.
Sequence in context: A091801 A050919 A341965 * A376101 A293145 A305919
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 16 2013
STATUS
approved