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A264462 Number of permutations of [n] with exactly three (possibly overlapping) occurrences of the generalized pattern 23-1.

%I A264462 #7 Nov 14 2015 16:51:00
%S A264462 10,98,791,6082,46508,360376,2855580,23244370,194796665,1682243510,
%T A264462 14973751272,137345968648,1297620307926,12620234271634,
%U A264462 126265094967383,1298634572382618,13720327052477584,148800093788609512,1655374072150829472,18877499531817214482
%N A264462 Number of permutations of [n] with exactly three (possibly overlapping) occurrences of the generalized pattern 23-1.
%H A264462 Alois P. Heinz, <a href="/A264462/b264462.txt">Table of n, a(n) for n = 5..500</a>
%e A264462 a(5) = 10: 23451, 24513, 24531, 34251, 35241, 45123, 45132, 45213, 45312, 45321.
%p A264462 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
%p A264462       b(u-j, o+j-1), j=1..u) +add(convert(series(
%p A264462       b(u+j-1, o-j)*x^u, x, 4), polynom), j=1..o))
%p A264462     end:
%p A264462 a:= n-> coeff(b(n, 0), x, 3):
%p A264462 seq(a(n), n=5..25);
%Y A264462 Column k=3 of A260670.
%K A264462 nonn
%O A264462 5,1
%A A264462 _Alois P. Heinz_, Nov 14 2015