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A230345 Number of permutations of [2n+5] in which the longest increasing run has length n+5.

%I A230345 #6 Oct 17 2013 14:57:04
%S A230345 1,12,181,3322,72540,1845480,53749920,1766525760,64739122560,
%T A230345 2619453513600,116043825744000,5588681114016000,290812286052288000,
%U A230345 16263827918642304000,973009916329651200000,62017234027123415040000,4195886889891954216960000
%N A230345 Number of permutations of [2n+5] in which the longest increasing run has length n+5.
%C A230345 Also the number of ascending runs of length n+5 in the permutations of [2n+5].
%H A230345 Alois P. Heinz, <a href="/A230345/b230345.txt">Table of n, a(n) for n = 0..300</a>
%F A230345 a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.
%F A230345 a(n) = A008304(2*n+5,n+5) = A122843(2*n+5,n+5).
%p A230345 a:= proc(n) option remember; `if`(n<2, 1+11*n, 2*(2*n+5)*(n+2)*
%p A230345       (n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))
%p A230345     end:
%p A230345 seq(a(n), n=0..25);
%Y A230345 A diagonal of A008304, A122843.
%K A230345 nonn
%O A230345 0,2
%A A230345 _Alois P. Heinz_, Oct 16 2013