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A230348 Number of permutations of [2n+8] in which the longest increasing run has length n+8.

%I A230348 #6 Oct 17 2013 15:05:26
%S A230348 1,18,349,7672,192240,5454144,173606040,6143195520,239656253760,
%T A230348 10231052832000,474832908950400,23819880180096000,1284985968634368000,
%U A230348 74207855717259264000,4569213387521502720000,298885288012537901875200,20702796608070625112064000
%N A230348 Number of permutations of [2n+8] in which the longest increasing run has length n+8.
%C A230348 Also the number of ascending runs of length n+8 in the permutations of [2n+8].
%H A230348 Alois P. Heinz, <a href="/A230348/b230348.txt">Table of n, a(n) for n = 0..300</a>
%F A230348 a(n) = (n^3+18*n^2+90*n+89)*(2*n+8)!/(n+10)! for n>0, a(0) = 1.
%F A230348 a(n) = A008304(2*n+8,n+8) = A122843(2*n+8,n+8).
%p A230348 a:= proc(n) option remember; `if`(n<2, 1+17*n, 2*(n+4)*(2*n+7)*
%p A230348       (n^3+18*n^2+90*n+89)*a(n-1)/((n+10)*(n^3+15*n^2+57*n+16)))
%p A230348     end:
%p A230348 seq(a(n), n=0..25);
%Y A230348 A diagonal of A008304, A122843.
%K A230348 nonn
%O A230348 0,2
%A A230348 _Alois P. Heinz_, Oct 16 2013