%I #4 Jul 25 2018 16:53:12

%S 1385,31493,460929,6632158,99592344,1489928080,22566676855,

%T 354404597721,5758011600442,96477356811365,1673128285327455,

%U 30065282456829860,558998263719383722,10749166166477149832,213755085162112473899,4392507334767609209209,93197430506980061714657

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

%H Alois P. Heinz, <a href="/A317284/b317284.txt">Table of n, a(n) for n = 8..471</a>

%p b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,

%p add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+

%p add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 5)

%p end:

%p a:= n-> coeff(b(n, 0$2), x, 4):

%p seq(a(n), n=8..30);

%Y Column k=4 of A097592.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Jul 25 2018