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A264457 Number of permutations of [n] with exactly eight (possibly overlapping) occurrences of the generalized pattern 12-3.

%I A264457 #6 Nov 14 2015 08:19:54
%S A264457 2,68,1303,19637,259676,3187742,37608672,435669452,5021292420,
%T A264457 58054439247,676861345712,7985430177542,95546837440564,
%U A264457 1161199181184289,14348225375153127,180370057811385955,2307651822107975903,30054039071752083133,398467881283163344126
%N A264457 Number of permutations of [n] with exactly eight (possibly overlapping) occurrences of the generalized pattern 12-3.
%H A264457 Alois P. Heinz, <a href="/A264457/b264457.txt">Table of n, a(n) for n = 6..500</a>
%e A264457 a(6) = 2: 123546, 123564.
%e A264457 a(7) = 68: 1243756, 1243765, 1247365, ..., 6123574, 7123546, 7123564.
%p A264457 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
%p A264457        b(u-j, o+j-1), j=1..u)+add(convert(series(
%p A264457        b(u+j-1, o-j)*x^(o-j), x, 9), polynom), j=1..o))
%p A264457     end:
%p A264457 a:= n-> coeff(b(n, 0), x, 8):
%p A264457 seq(a(n), n=6..25);
%Y A264457 Column k=8 of A260665.
%K A264457 nonn
%O A264457 6,1
%A A264457 _Alois P. Heinz_, Nov 14 2015