A263886 Number of permutations of [n] containing exactly two occurrences of the consecutive pattern 132.

3, 56, 753, 9024, 104814, 1228608, 14824314, 185991936, 2438459325, 33476112000, 481470208575, 7252002478080, 114295913943660, 1882806417303552, 32377593994012260, 580478495476948992, 10835925949596420135, 210343353555466229760, 4240673559279540077085

Offset: 5

Author

Alois P. Heinz, Oct 28 2015

Keywords

• nonn

Examples

			a(5) = 3: 13254, 14253, 15243.
a(6) = 56: 124365, 125364, 126354, ..., 613254, 614253, 615243.
a(7) = 753: 1235476, 1236475, 1237465, ..., 7613254, 7614253, 7615243.
a(8) = 9024: 12346587, 12347586, 12348576, ..., 87613254, 87614253, 87615243.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..200

Crossrefs

Column k=2 of A197365.

Programs

Maple

b:= proc(u, o, t) option remember; series(`if`(u+o=0, 1,
      add(b(u-j, o+j-1, 0)*`if`(j<=t, x, 1), j=1..u)+
      add(b(u+j-1, o-j, j-1), j=1..o)), x, 3)
    end:
a:= n-> coeff(b(n, 0$2), x, 2):
seq(a(n), n=5..30);

Formula

a(n) = A197365(n,2).