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%I #4 Jul 25 2018 16:46:13
%S 2702765,117248463,3118257980,73830310655,1708350797975,
%T 38581706239634,861226758827324,19346584353278646,439935779491790415,
%U 10146028258663315691,238129724283103648476,5701793180421505562215,139409020095464012520967,3483089247393778028230622
%N Number of permutations of [n] with exactly six increasing runs of even length.
%H Alois P. Heinz, <a href="/A317286/b317286.txt">Table of n, a(n) for n = 12..470</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, 7)
%p end:
%p a:= n-> coeff(b(n, 0$2), x, 6):
%p seq(a(n), n=12..30);
%Y Column k=6 of A097592.
%K nonn
%O 12,1
%A _Alois P. Heinz_, Jul 25 2018
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