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A317285 Number of permutations of [n] with exactly five increasing runs of even length.

%I A317285 #6 Jul 25 2018 16:49:10
%S A317285 50521,1629248,32918922,617859020,11668739836,217316513198,
%T A317285 4043244094251,76688877688570,1487035437929625,29470163960950720,
%U A317285 598896893196470516,12504145259394103084,268208623687371202156,5911352523792061709194,133914475861667199021171
%N A317285 Number of permutations of [n] with exactly five increasing runs of even length.
%H A317285 Alois P. Heinz, <a href="/A317285/b317285.txt">Table of n, a(n) for n = 10..470</a>
%p A317285 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317285       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317285       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 6)
%p A317285     end:
%p A317285 a:= n-> coeff(b(n, 0$2), x, 5):
%p A317285 seq(a(n), n=10..30);
%Y A317285 Column k=5 of A097592.
%K A317285 nonn
%O A317285 10,1
%A A317285 _Alois P. Heinz_, Jul 25 2018