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!)
A133221 A001147 with each term repeated. 7
1, 1, 1, 1, 3, 3, 15, 15, 105, 105, 945, 945, 10395, 10395, 135135, 135135, 2027025, 2027025, 34459425, 34459425, 654729075, 654729075, 13749310575, 13749310575, 316234143225, 316234143225, 7905853580625, 7905853580625, 213458046676875, 213458046676875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Normally such sequences are excluded from the OEIS, but I have made an exception for this one because so many variants of it have occurred in recent submissions.

For n>=2, a(n) = product of odd positive integers <=(n-1). - Jaroslav Krizek, Mar 21 2009

a(n) is, for n>=3, the number of way to choose floor((n-1)/2) disjoint pairs of items from n-1 items. It is then a fortiori the size of the conjugacy class of the reversal permutation [n-1,n-2,n-3,...,3,2,1]=(1 n-1)(2 n-2)(3 n-3)... in the symmetric group on n-1 elements. - Karl-Dieter Crisman, Nov 03 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..800

FORMULA

E.g.f.: x*U(0)  where U(k)= 1 + (2*k+1)/(x - x^4/(x^3 + (2*k+2)*(2*k+3)/U(k+1))) ; (continued fraction, 3rd kind, 3-step). - Sergei N. Gladkovskii, Sep 25 2012

G.f.: 1+x*G(0), where G(k)= 1 + x*(2*k+1)/(1 - x/(x + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013

MATHEMATICA

f[x_] := E^(x^2/2) + Sqrt[Pi/2]*Erfi[x/Sqrt[2]]; CoefficientList[ Series[f[x], {x, 0, 29}], x]*Range[0, 29]! (* Jean-Fran├žois Alcover, Sep 25 2012, after Sergei N. Gladkovskii *)

Table[(n - 1 - Mod[n, 2])!!, {n, 0, 20}] (* Eric W. Weisstein, Dec 31 2017 *)

Table[((2 n + (-1)^n - 3)/2)!!, {n, 0, 20}] (* Eric W. Weisstein, Dec 31 2017 *)

PROG

(Sage)

def Gauss_factorial(N, n): return mul(j for j in (1..N) if gcd(j, n) == 1)

def A133221(n): return Gauss_factorial(n-1, 2)

[A133221(n) for n in (0..29)]  # Peter Luschny, Oct 01 2012

(PARI) a(n) = my(k = (2*n + (-1)^n - 3)/2); prod(i=0, (k-1)\2, k - 2*i) \\ Iain Fox, Dec 31 2017

CROSSREFS

Cf. A055634.

Appears in A161736. - Johannes W. Meijer, Jun 18 2009

Sequence in context: A217858 A185275 A055634 * A232097 A110096 A157526

Adjacent sequences:  A133218 A133219 A133220 * A133222 A133223 A133224

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 13 2007

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 April 23 06:38 EDT 2021. Contains 343201 sequences. (Running on oeis4.)