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A230345 Number of permutations of [2n+5] in which the longest increasing run has length n+5. 3

%I

%S 1,12,181,3322,72540,1845480,53749920,1766525760,64739122560,

%T 2619453513600,116043825744000,5588681114016000,290812286052288000,

%U 16263827918642304000,973009916329651200000,62017234027123415040000,4195886889891954216960000

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

%C Also the number of ascending runs of length n+5 in the permutations of [2n+5].

%H Alois P. Heinz, <a href="/A230345/b230345.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = (n^3+12*n^2+42*n+41)*(2*n+5)!/(n+7)! for n>0, a(0) = 1.

%F a(n) = A008304(2*n+5,n+5) = A122843(2*n+5,n+5).

%p a:= proc(n) option remember; `if`(n<2, 1+11*n, 2*(2*n+5)*(n+2)*

%p (n^3+12*n^2+42*n+41)*a(n-1)/((n+7)*(n^3+9*n^2+21*n+10)))

%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 June 6 16:22 EDT 2020. Contains 334828 sequences. (Running on oeis4.)