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A317284 Number of permutations of [n] with exactly four increasing runs of even length.

%I A317284 #4 Jul 25 2018 16:53:12
%S A317284 1385,31493,460929,6632158,99592344,1489928080,22566676855,
%T A317284 354404597721,5758011600442,96477356811365,1673128285327455,
%U A317284 30065282456829860,558998263719383722,10749166166477149832,213755085162112473899,4392507334767609209209,93197430506980061714657
%N A317284 Number of permutations of [n] with exactly four increasing runs of even length.
%H A317284 Alois P. Heinz, <a href="/A317284/b317284.txt">Table of n, a(n) for n = 8..471</a>
%p A317284 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317284       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317284       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 5)
%p A317284     end:
%p A317284 a:= n-> coeff(b(n, 0$2), x, 4):
%p A317284 seq(a(n), n=8..30);
%Y A317284 Column k=4 of A097592.
%K A317284 nonn
%O A317284 8,1
%A A317284 _Alois P. Heinz_, Jul 25 2018