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A264459 Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 12-3.

%I A264459 #6 Nov 14 2015 08:07:36
%S A264459 1,28,594,10735,169753,2438911,32897588,427124523,5433554133,
%T A264459 68546679923,864462182024,10957001813778,140087846414020,
%U A264459 1811142056680743,23718822943004668,315018653189118579,4246519279200474842,58132401024629625298,808428792791995327013
%N A264459 Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 12-3.
%H A264459 Alois P. Heinz, <a href="/A264459/b264459.txt">Table of n, a(n) for n = 6..500</a>
%e A264459 a(6) = 1: 123456.
%e A264459 a(7) = 28: 1236475, 1236547, 1236574, 1236745, 1236754, 1237456, 1243576, 1245376, 1245736, 1245763, 1246357, 1253467, 1324567, 1342567, 1345267, 1345627, 1345672, 2134567, 2314567, 2341567, 2345167, 2345617, 2345671, 3124567, 4123567, 5123467, 6123457, 7123456.
%p A264459 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(
%p A264459        b(u-j, o+j-1), j=1..u)+add(convert(series(
%p A264459        b(u+j-1, o-j)*x^(o-j), x, 11), polynom), j=1..o))
%p A264459     end:
%p A264459 a:= n-> coeff(b(n, 0), x, 10):
%p A264459 seq(a(n), n=6..25);
%Y A264459 Column k=10 of A260665.
%K A264459 nonn
%O A264459 6,2
%A A264459 _Alois P. Heinz_, Nov 14 2015