A263885 Number of permutations of [n] containing exactly one occurrence of the consecutive pattern 132.

1, 8, 54, 368, 2649, 20544, 172596, 1569408, 15398829, 162412416, 1834081890, 22093090560, 282889238253, 3837991053312, 55010010678120, 830731742908416, 13185328329110745, 219457733809563648, 3822426663111579150, 69538569862816419840, 1318999546575572747265

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..200

Eric Weisstein's World of Mathematics, Inverse Erf

Formula

a(n) = A197365(n,1).

a(n) ~ c * d^n * n! * n, where d = 1/A240885 = 1/(sqrt(2) * InverseErf(sqrt(2/Pi))) = 0.78397693120354749... and c = 0.679554202696108785... . - Vaclav Kotesovec, Oct 29 2015

Example

a(3) = 1: 132.
a(4) = 8: 1243, 1324, 1423, 1432, 2143, 2431, 3142, 4132.
a(5) = 54: 12354, 12435, 12534, ..., 52431, 53142, 54132.
a(6) = 368: 123465, 123546, 123645, ..., 652431, 653142, 654132.
a(7) = 2649: 1234576, 1234657, 1234756, ..., 7652431, 7653142, 7654132.

Maple

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

Mathematica

Drop[Coefficient[CoefficientList[Series[1/(1 - (Sqrt[Pi/2]*Erfi[(Sqrt[u-1]*x) / Sqrt[2]])/Sqrt[u-1]), {x, 0, 25}], x] * Range[0, 25]!, u], 3] (* Vaclav Kotesovec, Oct 29 2015 *)

Crossrefs

Column k=1 of A197365.

Sequence in context: A289796 A287814 A201640 * A002775 A079754 A347274

Adjacent sequences: A263882 A263883 A263884 * A263886 A263887 A263888

Keyword

nonn

Author

Alois P. Heinz, Oct 28 2015

Status

approved