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A317288 Number of permutations of [n] with exactly eight increasing runs of even length.

%I A317288 #4 Jul 25 2018 16:41:54
%S A317288 19391512145,1367267690953,57188581537971,2006576231088264,
%T A317288 65823539327956911,2066450841399035025,63056350327027739274,
%U A317288 1900463594609383889937,57088794679037177345346,1717519261928956311195227,51966007918370324842446184,1586467824560962829102119877
%N A317288 Number of permutations of [n] with exactly eight increasing runs of even length.
%H A317288 Alois P. Heinz, <a href="/A317288/b317288.txt">Table of n, a(n) for n = 16..469</a>
%p A317288 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317288       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317288       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 9)
%p A317288     end:
%p A317288 a:= n-> coeff(b(n, 0$2), x, 8):
%p A317288 seq(a(n), n=16..30);
%Y A317288 Column k=8 of A097592.
%K A317288 nonn
%O A317288 16,1
%A A317288 _Alois P. Heinz_, Jul 25 2018