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A230347 Number of permutations of [2n+7] in which the longest increasing run has length n+7.

%I A230347 #6 Oct 17 2013 15:00:35
%S A230347 1,16,287,5954,142590,3900480,120466080,4156079760,158664456720,
%T A230347 6647965632000,303540020784000,15009431909472000,799414492260384000,
%U A230347 45641465547245568000,2781538377619921920000,180263592116387619840000,12381113998069012804608000
%N A230347 Number of permutations of [2n+7] in which the longest increasing run has length n+7.
%C A230347 Also the number of ascending runs of length n+7 in the permutations of [2n+7].
%H A230347 Alois P. Heinz, <a href="/A230347/b230347.txt">Table of n, a(n) for n = 0..300</a>
%F A230347 a(n) = (n^3+16*n^2+72*n+71)*(2*n+7)!/(n+9)! for n>0, a(0) = 1.
%F A230347 a(n) = A008304(2*n+7,n+7) = A122843(2*n+7,n+7).
%p A230347 a:= proc(n) option remember; `if`(n<2, 1+15*n, 2*(n+3)*(2*n+7)*
%p A230347       (n^3+16*n^2+72*n+71)*a(n-1)/((n+9)*(n^3+13*n^2+43*n+14)))
%p A230347     end:
%p A230347 seq(a(n), n=0..25);
%Y A230347 A diagonal of A008304, A122843.
%K A230347 nonn
%O A230347 0,2
%A A230347 _Alois P. Heinz_, Oct 16 2013