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Number of permutations of [2n+9] in which the longest increasing run has length n+9.
3

%I #6 Oct 17 2013 15:07:14

%S 1,20,417,9690,253776,7465176,244906200,8891411760,354610872000,

%T 15432114297600,728406536457600,37090538241120000,2027740775284224000,

%U 118512161081233920000,7376476698319125196800,487273386402209523916800,34055074238462266429440000

%N Number of permutations of [2n+9] in which the longest increasing run has length n+9.

%C Also the number of ascending runs of length n+9 in the permutations of [2n+9].

%H Alois P. Heinz, <a href="/A230349/b230349.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = (n^3+20*n^2+110*n+109)*(2*n+9)!/(n+11)! for n>0, a(0) = 1.

%F a(n) = A008304(2*n+9,n+9) = A122843(2*n+9,n+9).

%p a:= proc(n) option remember; `if`(n<2, 1+19*n, 2*(2*n+9)*(n+4)*

%p (n^3+20*n^2+110*n+109)*a(n-1)/((n+11)*(n^3+17*n^2+73*n+18)))

%p end:

%p seq(a(n), n=0..25);

%Y A diagonal of A008304, A122843.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 16 2013