cp's OEIS Frontend

A230342 Number of permutations of [2n+2] in which the longest increasing run has length n+2.

%I A230342 #9 Oct 17 2013 14:44:47
%S A230342 1,6,67,1024,19710,456720,12372360,383685120,13406178240,521194867200,
%T A230342 22318001798400,1043827513344000,52949040240096000,
%U A230342 2895555891900672000,169823181579891840000,10633812541718446080000,708077586604965857280000,49962245750984840232960000
%N A230342 Number of permutations of [2n+2] in which the longest increasing run has length n+2.
%C A230342 Also the number of ascending runs of length n+2 in the permutations of [2n+2].
%H A230342 Alois P. Heinz, <a href="/A230342/b230342.txt">Table of n, a(n) for n = 0..300</a>
%F A230342 a(n) = (n^3+6*n^2+12*n+11)*(2*n+2)!/(n+4)! for n>0, a(0) = 1.
%F A230342 a(n) = A008304(2*n+2,n+2) = A122843(2*n+2,n+2).
%p A230342 a:= proc(n) option remember; `if`(n<2, 1+5*n, 2*(n+1)*(2*n+1)*
%p A230342       (n^3+6*n^2+12*n+11)*a(n-1)/((n+4)*(n^3+3*n^2+3*n+4)))
%p A230342     end:
%p A230342 seq(a(n), n=0..25);
%Y A230342 A diagonal of A008304, A122843.
%K A230342 nonn
%O A230342 0,2
%A A230342 _Alois P. Heinz_, Oct 16 2013