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 A230346 Number of permutations of [2n+6] in which the longest increasing run has length n+6. 3

%I

%S 1,14,231,4512,103194,2721600,81591840,2746068480,102661518960,

%T 4224849995520,189917647920000,9263565222912000,487461283781472000,

%U 27533206366009344000,1661865400404937728000,106768864984887705600000,7275718977990226283520000

%N Number of permutations of [2n+6] in which the longest increasing run has length n+6.

%C Also the number of ascending runs of length n+6 in the permutations of [2n+6].

%H Alois P. Heinz, <a href="/A230346/b230346.txt">Table of n, a(n) for n = 0..300</a>

%F a(n) = (n+5)*(n^2+9*n+11)*(2*n+6)!/(n+8)! for n>0, a(0) = 1.

%F a(n) = A008304(2*n+6,n+6) = A122843(2*n+6,n+6).

%p a:= proc(n) option remember; `if`(n<2, 1+13*n, 2*(2*n+5)*(n+5)*

%p (n+3)*(n^2+9*n+11)*a(n-1)/((n+4)*(n+8)*(n^2+7*n+3)))

%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 October 15 18:11 EDT 2019. Contains 328037 sequences. (Running on oeis4.)