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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103639 Product_{i=1..2n} 2*i+1. 6
1, 15, 945, 135135, 34459425, 13749310575, 7905853580625, 6190283353629375, 6332659870762850625, 8200794532637891559375, 13113070457687988603440625, 25373791335626257947657609375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..11.

FORMULA

a(n) = (4n+2)! / [2 * 4^n * (2n+1)! ].

E.g.f.: sinh(x^2/2) = x^2/2! + 15x^6/6! + 945x^10/10! +...

Recurrence: a(n+1) = (4n-1)(4n+1)*a(n), a(0) = 1.

a(n) = (4n+1)!!. - Vladimir Reshetnikov, Nov 03 2015

EXAMPLE

Sequence starts 1, 1*3*5, 1*3*5*7*9, 1*3*5*7*9*11*13, ...

MAPLE

A103639 := n -> pochhammer(1/2, 2*n+1)*2^(2*n+1): seq(A103639(n), n=0..11); # Peter Luschny, Dec 19 2012

MATHEMATICA

Table[(4n+1)!!, {n, 0, 15}] (* Vladimir Reshetnikov, Nov 03 2015 *)

PROG

(Sage)

def A103639(n):

    return falling_factorial(4*n+2, 2*n+1)*2^(-1-2*n)

print [A103639(n) for n in (0..11)]  # Peter Luschny, Dec 14 2012

(PARI) vector(20, n, n--; prod(i=1, 2*n, 2*i+1)) \\ Altug Alkan, Nov 04 2015

CROSSREFS

Bisection of the double factorials A001147. Cf. A102992.

Cf. Odd part of A024343 and A009564.

Sequence in context: A261067 A136419 A231121 * A055413 A067408 A274713

Adjacent sequences:  A103636 A103637 A103638 * A103640 A103641 A103642

KEYWORD

nonn

AUTHOR

Ralf Stephan, Feb 18 2005

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 January 17 12:18 EST 2020. Contains 330958 sequences. (Running on oeis4.)