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%I #6 Oct 17 2013 14:59:18
%S 1,14,231,4512,103194,2721600,81591840,2746068480,102661518960,
%T 4224849995520,189917647920000,9263565222912000,487461283781472000,
%U 27533206366009344000,1661865400404937728000,106768864984887705600000,7275718977990226283520000
%N Number of permutations of [2n+6] in which the longest increasing run has length n+6.
%C Also the number of ascending runs of length n+6 in the permutations of [2n+6].
%H Alois P. Heinz, <a href="/A230346/b230346.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = (n+5)*(n^2+9*n+11)*(2*n+6)!/(n+8)! for n>0, a(0) = 1.
%F a(n) = A008304(2*n+6,n+6) = A122843(2*n+6,n+6).
%p a:= proc(n) option remember; `if`(n<2, 1+13*n, 2*(2*n+5)*(n+5)*
%p (n+3)*(n^2+9*n+11)*a(n-1)/((n+4)*(n+8)*(n^2+7*n+3)))
%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