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A263886 Number of permutations of [n] containing exactly two occurrences of the consecutive pattern 132.

%I A263886 #6 Oct 28 2015 20:13:41
%S A263886 3,56,753,9024,104814,1228608,14824314,185991936,2438459325,
%T A263886 33476112000,481470208575,7252002478080,114295913943660,
%U A263886 1882806417303552,32377593994012260,580478495476948992,10835925949596420135,210343353555466229760,4240673559279540077085
%N A263886 Number of permutations of [n] containing exactly two occurrences of the consecutive pattern 132.
%H A263886 Alois P. Heinz, <a href="/A263886/b263886.txt">Table of n, a(n) for n = 5..200</a>
%F A263886 a(n) = A197365(n,2).
%e A263886 a(5) = 3: 13254, 14253, 15243.
%e A263886 a(6) = 56: 124365, 125364, 126354, ..., 613254, 614253, 615243.
%e A263886 a(7) = 753: 1235476, 1236475, 1237465, ..., 7613254, 7614253, 7615243.
%e A263886 a(8) = 9024: 12346587, 12347586, 12348576, ..., 87613254, 87614253, 87615243.
%p A263886 b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
%p A263886       add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
%p A263886       add(b(u+j-1, o-j, j-1), j=1..o)), x, 3)
%p A263886     end:
%p A263886 a:= n-> coeff(b(n, 0$2), x, 2):
%p A263886 seq(a(n), n=5..30);
%Y A263886 Column k=2 of A197365.
%K A263886 nonn
%O A263886 5,1
%A A263886 _Alois P. Heinz_, Oct 28 2015