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A103639 Product_{i=1..2n} 2*i+1. 6

%I

%S 1,15,945,135135,34459425,13749310575,7905853580625,6190283353629375,

%T 6332659870762850625,8200794532637891559375,

%U 13113070457687988603440625,25373791335626257947657609375

%N Product_{i=1..2n} 2*i+1.

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

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

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

%F a(n) = (4n+1)!!. - _Vladimir Reshetnikov_, Nov 03 2015

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

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

%t Table[(4n+1)!!, {n, 0, 15}] (* _Vladimir Reshetnikov_, Nov 03 2015 *)

%o (Sage)

%o def A103639(n):

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

%o print [A103639(n) for n in (0..11)] # _Peter Luschny_, Dec 14 2012

%o (PARI) vector(20, n, n--; prod(i=1, 2*n, 2*i+1)) \\ _Altug Alkan_, Nov 04 2015

%Y Bisection of the double factorials A001147. Cf. A102992.

%Y Cf. Odd part of A024343 and A009564.

%K nonn

%O 0,2

%A _Ralf Stephan_, Feb 18 2005

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Last modified February 20 20:55 EST 2020. Contains 332084 sequences. (Running on oeis4.)