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A317282 Number of permutations of [n] with exactly two increasing runs of even length.

%I A317282 #4 Jul 25 2018 16:56:49
%S A317282 5,43,258,1853,15634,133697,1207256,11974457,126980013,1421291622,
%T A317282 16925790480,213992804118,2851968574855,39996895523591,
%U A317282 589713707701692,9114791365659163,147335664946835342,2486973983349027871,43763134470537718258,801419373432471123541
%N A317282 Number of permutations of [n] with exactly two increasing runs of even length.
%H A317282 Alois P. Heinz, <a href="/A317282/b317282.txt">Table of n, a(n) for n = 4..472</a>
%p A317282 b:= proc(u, o, t) option remember; series(`if`(u+o=0, x^t,
%p A317282       add(b(u+j-1, o-j, irem(t+1, 2)), j=1..o)+
%p A317282       add(b(u-j, o+j-1, 0)*x^t, j=1..u)), x, 3)
%p A317282     end:
%p A317282 a:= n-> coeff(b(n, 0$2), x, 2):
%p A317282 seq(a(n), n=4..30);
%Y A317282 Column k=2 of A097592.
%K A317282 nonn
%O A317282 4,1
%A A317282 _Alois P. Heinz_, Jul 25 2018