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%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
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