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a(n) = product of n successive numbers up to n, if n is even a(n) = n*(n-1)*.. = n!,if n is odd a(n) = n(n+1)(n+2)... 'n' terms.
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%I #6 May 06 2017 23:40:50

%S 1,2,60,24,15120,720,8648640,40320,8821612800,3628800,14079294028800,

%T 479001600,32382376266240000,87178291200,101421602465863680000,

%U 20922789888000,415017197290314178560000,6402373705728000,2149789081963827444940800000

%N a(n) = product of n successive numbers up to n, if n is even a(n) = n*(n-1)*.. = n!,if n is odd a(n) = n(n+1)(n+2)... 'n' terms.

%C a(2n)*a(2n+1) = (4n+1)!. a(2)*a(3) = 5!, a(4)*a(5) = 9!.

%H G. C. Greubel, <a href="/A113549/b113549.txt">Table of n, a(n) for n = 1..350</a>

%F a(1) = 1, a(2n) = (2n)!, a(2n-1) = (4n-3)!/(2n-2)!.

%e a(3) = 3*4*5 = 60, a(4)= 4*3*2*1 24.

%t n = 1; anfunc[n_] := (If [OddQ[n], {an = n, Do[an = an*(n + i), {i, n - 1}]}, an = n! ]; an) Table[anfunc[n], {n, 1, 30}] - Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006

%Y Cf. A113550.

%K easy,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 03 2005

%E More terms from Elizabeth A. Blickley (Elizabeth.Blickley(AT)gmail.com), Mar 10 2006