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A230349 Number of permutations of [2n+9] in which the longest increasing run has length n+9.

%I A230349 #6 Oct 17 2013 15:07:14
%S A230349 1,20,417,9690,253776,7465176,244906200,8891411760,354610872000,
%T A230349 15432114297600,728406536457600,37090538241120000,2027740775284224000,
%U A230349 118512161081233920000,7376476698319125196800,487273386402209523916800,34055074238462266429440000
%N A230349 Number of permutations of [2n+9] in which the longest increasing run has length n+9.
%C A230349 Also the number of ascending runs of length n+9 in the permutations of [2n+9].
%H A230349 Alois P. Heinz, <a href="/A230349/b230349.txt">Table of n, a(n) for n = 0..300</a>
%F A230349 a(n) = (n^3+20*n^2+110*n+109)*(2*n+9)!/(n+11)! for n>0, a(0) = 1.
%F A230349 a(n) = A008304(2*n+9,n+9) = A122843(2*n+9,n+9).
%p A230349 a:= proc(n) option remember; `if`(n<2, 1+19*n, 2*(2*n+9)*(n+4)*
%p A230349       (n^3+20*n^2+110*n+109)*a(n-1)/((n+11)*(n^3+17*n^2+73*n+18)))
%p A230349     end:
%p A230349 seq(a(n), n=0..25);
%Y A230349 A diagonal of A008304, A122843.
%K A230349 nonn
%O A230349 0,2
%A A230349 _Alois P. Heinz_, Oct 16 2013