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

%I #9 Nov 14 2015 08:21:15

%S 5,122,1960,25922,308912,3488684,38438284,420224213,4604712333,

%T 50891058160,569534211553,6470640729869,74755213239764,

%U 879145839345147,10531462769901577,128554339635477023,1599307831822386125,20278763016658278490,262052769447634167173

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

%H Alois P. Heinz, <a href="/A264456/b264456.txt">Table of n, a(n) for n = 6..500</a>

%e a(6) = 5: 123645, 123654, 124356, 124536, 124563.

%e a(7) = 122: 1253746, 1253764, 1254376, ..., 7124356, 7124536, 7124563.

%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, 8), polynom), j=1..o))

%p end:

%p a:= n-> coeff(b(n, 0), x, 7):

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

%Y Column k=7 of A260665.

%K nonn

%O 6,1

%A _Alois P. Heinz_, Nov 14 2015