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A230382 Number of ascending runs of length n in the permutations of [2n].

%I A230382 #7 Oct 18 2013 04:48:19
%S A230382 1,2,21,312,5880,133920,3575880,109549440,3788104320,145957593600,
%T A230382 6201593798400,288084016281600,14525808782284800,790129980896256000,
%U A230382 46120599397192320000,2875600728738017280000,190740227037467627520000,13411608375592258191360000
%N A230382 Number of ascending runs of length n in the permutations of [2n].
%H A230382 Alois P. Heinz, <a href="/A230382/b230382.txt">Table of n, a(n) for n = 0..300</a>
%F A230382 For n>0, a(n) = (n^2+n+1)*(2*n)!/((n+2)*n!). - _Vaclav Kotesovec_, Oct 18 2013
%p A230382 a:= proc(n) option remember; `if`(n<2, 1+n,
%p A230382       2*(2*n-1)*(n+1)*(n^2+n+1)*a(n-1)/((n+2)*(n^2-n+1)))
%p A230382     end:
%p A230382 seq(a(n), n=0..25);
%Y A230382 A diagonal of A122843.
%K A230382 nonn
%O A230382 0,2
%A A230382 _Alois P. Heinz_, Oct 17 2013