%I #6 Oct 17 2013 14:49:00
%S 1,10,137,2360,49236,1209936,34288800,1102187520,39656131200,
%T 1579837754880,69064610186880,3288126441600000,169388400557376000,
%U 9389435419203840000,557323393281887232000,35272416767753797632000,2371290445442664345600000
%N Number of permutations of [2n+4] in which the longest increasing run has length n+4.
%C Also the number of ascending runs of length n+4 in the permutations of [2n+4].
%H Alois P. Heinz, <a href="/A230344/b230344.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = (n^3+10*n^2+30*n+29)*(2*n+4)!/(n+6)! for n>0, a(0) = 1.
%F a(n) = A008304(2*n+4,n+4) = A122843(2*n+4,n+4).
%p a:= proc(n) option remember; `if`(n<2, 1+9*n, 2*(2*n+3)*(n+2)*
%p (n^3+10*n^2+30*n+29)*a(n-1)/((n+6)*(n^3+7*n^2+13*n+8)))
%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