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Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 12-3.
2

%I #6 Nov 14 2015 08:07:36

%S 1,28,594,10735,169753,2438911,32897588,427124523,5433554133,

%T 68546679923,864462182024,10957001813778,140087846414020,

%U 1811142056680743,23718822943004668,315018653189118579,4246519279200474842,58132401024629625298,808428792791995327013

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

%H Alois P. Heinz, <a href="/A264459/b264459.txt">Table of n, a(n) for n = 6..500</a>

%e a(6) = 1: 123456.

%e 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 b:= proc(u, o) option remember; `if`(u+o=0, 1, add(

%p b(u-j, o+j-1), j=1..u)+add(convert(series(

%p b(u+j-1, o-j)*x^(o-j), x, 11), polynom), j=1..o))

%p end:

%p a:= n-> coeff(b(n, 0), x, 10):

%p seq(a(n), n=6..25);

%Y Column k=10 of A260665.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Nov 14 2015