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A230348 Number of permutations of [2n+8] in which the longest increasing run has length n+8. 3

%I

%S 1,18,349,7672,192240,5454144,173606040,6143195520,239656253760,

%T 10231052832000,474832908950400,23819880180096000,1284985968634368000,

%U 74207855717259264000,4569213387521502720000,298885288012537901875200,20702796608070625112064000

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

%C Also the number of ascending runs of length n+8 in the permutations of [2n+8].

%H Alois P. Heinz, <a href="/A230348/b230348.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = (n^3+18*n^2+90*n+89)*(2*n+8)!/(n+10)! for n>0, a(0) = 1.

%F a(n) = A008304(2*n+8,n+8) = A122843(2*n+8,n+8).

%p a:= proc(n) option remember; `if`(n<2, 1+17*n, 2*(n+4)*(2*n+7)*

%p (n^3+18*n^2+90*n+89)*a(n-1)/((n+10)*(n^3+15*n^2+57*n+16)))

%p end:

%p seq(a(n), n=0..25);

%Y A diagonal of A008304, A122843.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 16 2013

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)