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A230343 Number of permutations of [2n+3] in which the longest increasing run has length n+3.

%I A230343 #8 Oct 17 2013 14:46:06
%S A230343 1,8,99,1602,32010,761904,21064680,663848640,23500653120,923616691200,
%T A230343 39914540709120,1881558401184000,96096062174112000,
%U A230343 5286518167746816000,311689569962010240000,19608741674518284288000,1311187373310480906240000,92868537238628772741120000
%N A230343 Number of permutations of [2n+3] in which the longest increasing run has length n+3.
%C A230343 Also the number of ascending runs of length n+3 in the permutations of [2n+3].
%H A230343 Alois P. Heinz, <a href="/A230343/b230343.txt">Table of n, a(n) for n = 0..300</a>
%F A230343 a(n) = (n^3+8*n^2+20*n+19)*(2*n+3)!/(n+5)! for n>0, a(0) = 1.
%F A230343 a(n) = A008304(2*n+3,n+3) = A122843(2*n+3,n+3).
%p A230343 a:= proc(n) option remember; `if`(n<2, 1+7*n, 2*(2*n+3)*(n+1)*
%p A230343       (n^3+8*n^2+20*n+19)*a(n-1)/((n+5)*(n^3+5*n^2+7*n+6)))
%p A230343     end:
%p A230343 seq(a(n), n=0..25);
%Y A230343 A diagonal of A008304, A122843.
%K A230343 nonn
%O A230343 0,2
%A A230343 _Alois P. Heinz_, Oct 16 2013