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A264451 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of the generalized pattern 12-3.

%I A264451 #7 Nov 14 2015 08:03:43
%S A264451 1,13,112,843,6089,43887,321357,2411686,18631631,148490575,1221894598,
%T A264451 10382648734,91073271181,824221683639,7690752545310,73932347642395,
%U A264451 731636916804531,7447376286108705,77913394499688645,837113596053971008,9229808681562243113
%N A264451 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of the generalized pattern 12-3.
%H A264451 Alois P. Heinz, <a href="/A264451/b264451.txt">Table of n, a(n) for n = 4..500</a>
%e A264451 a(4) = 1: 1243.
%e A264451 a(5) = 13: 13254, 13524, 13542, 14235, 21354, 23154, 23514, 23541, 24135, 31254, 34125, 41253, 51243.
%p A264451 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
%p A264451        b(u-j, o+j-1), j=1..u)+add(convert(series(
%p A264451        b(u+j-1, o-j)*x^(o-j), x, 3), polynom), j=1..o))
%p A264451     end:
%p A264451 a:= n-> coeff(b(n, 0), x, 2):
%p A264451 seq(a(n), n=4..25);
%Y A264451 Column k=2 of A260665.
%K A264451 nonn
%O A264451 4,2
%A A264451 _Alois P. Heinz_, Nov 14 2015