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A230350 Number of permutations of [2n+10] in which the longest increasing run has length n+10.

%I A230350 #6 Oct 17 2013 15:11:04
%S A230350 1,22,491,12032,328950,10027440,339006360,12628788480,515033719200,
%T A230350 22855760928000,1097589192336000,56754471481344000,
%U A230350 3145763658989952000,186150029203211673600,11717355323144959488000,781981263963810054144000,55165533654753963657216000
%N A230350 Number of permutations of [2n+10] in which the longest increasing run has length n+10.
%C A230350 Also the number of ascending runs of length n+10 in the permutations of [2n+10].
%H A230350 Alois P. Heinz, <a href="/A230350/b230350.txt">Table of n, a(n) for n = 0..300</a>
%F A230350 a(n) = (n^3+22*n^2+132*n+131)*(2*n+10)!/(n+12)! for n>0, a(0) = 1.
%F A230350 a(n) = A008304(2*n+10,n+10) = A122843(2*n+10,n+10).
%p A230350 a:= proc(n) option remember; `if`(n<2, 1+21*n, 2*(n+5)*(2*n+9)*
%p A230350       (n^3+22*n^2+132*n+131)*a(n-1)/((n+12)*(n^3+19*n^2+91*n+20)))
%p A230350     end:
%p A230350 seq(a(n), n=0..25);
%Y A230350 A diagonal of A008304, A122843.
%K A230350 nonn
%O A230350 0,2
%A A230350 _Alois P. Heinz_, Oct 16 2013