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A317290 Number of permutations of [n] with exactly ten increasing runs of even length.

%I A317290 #5 Jul 25 2018 16:34:41
%S A317290 370371188237525,38563334673062963,2325983895636537462,
%T A317290 113126812608590106065,4980791141860424686096,
%U A317290 206198935127851667065607,8187758750644879282198684,316873661623427502461383547,12080329061828597152861716278,456708256439969037699279918515
%N A317290 Number of permutations of [n] with exactly ten increasing runs of even length.
%H A317290 Alois P. Heinz, <a href="/A317290/b317290.txt">Table of n, a(n) for n = 20..468</a>
%p A317290 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317290       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317290       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 11)
%p A317290     end:
%p A317290 a:= n-> coeff(b(n, 0$2), x, 10):
%p A317290 seq(a(n), n=20..30);
%Y A317290 Column k=10 of A097592.
%K A317290 nonn
%O A317290 20,1
%A A317290 _Alois P. Heinz_, Jul 25 2018