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Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 23-1.
2

%I #5 Nov 14 2015 17:01:15

%S 4,432,10723,185030,2679741,35436222,447105877,5525656829,67836294722,

%T 834260210092,10332749157300,129333951912536,1639800629344515,

%U 21092071947142268,275512690552878512,3657197040905519063,49353853545913899116,677272710732166102115

%N Number of permutations of [n] with exactly ten (possibly overlapping) occurrences of the generalized pattern 23-1.

%H Alois P. Heinz, <a href="/A264469/b264469.txt">Table of n, a(n) for n = 7..500</a>

%e a(7) = 4: 4567231, 5672341, 5673412, 5673421.

%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^u, x, 11), polynom), j=1..o))

%p end:

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

%p seq(a(n), n=7..25);

%Y Column k=10 of A260670.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Nov 14 2015