login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A263885 Number of permutations of [n] containing exactly one occurrence of the consecutive pattern 132. 3
1, 8, 54, 368, 2649, 20544, 172596, 1569408, 15398829, 162412416, 1834081890, 22093090560, 282889238253, 3837991053312, 55010010678120, 830731742908416, 13185328329110745, 219457733809563648, 3822426663111579150, 69538569862816419840, 1318999546575572747265 (list; graph; refs; listen; history; text; internal format)
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 A298985

Adjacent sequences:  A263882 A263883 A263884 * A263886 A263887 A263888

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 28 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 6 11:14 EDT 2020. Contains 336246 sequences. (Running on oeis4.)