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

%I #6 Nov 14 2015 08:17:21

%S 1,39,859,14531,211877,2822490,35642278,437300537,5296987965,

%T 63998700926,776411239316,9499309138937,117556007163447,

%U 1474385436584002,18766076242349261,242618101536221884,3187985361564230544,42590476320847716703,578630818810648513246

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

%H Alois P. Heinz, <a href="/A264458/b264458.txt">Table of n, a(n) for n = 6..500</a>

%e a(6) = 1: 123465.

%e a(7) = 39: 1237465, 1237546, 1237564, ..., 5123476, 6123475, 7123465.

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

%p end:

%p a:= n-> coeff(b(n, 0), x, 9):

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

%Y Column k=9 of A260665.

%K nonn

%O 6,2

%A _Alois P. Heinz_, Nov 14 2015