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%I #14 Jun 15 2016 09:23:10
%S 1,31,2745,487935,145769625,65830256415,41892106080825,
%T 35736278004165375,39370290736153001625,54420772423242699849375,
%U 92234193751998833171261625,188098544080793843475953349375,454418941572893462364414856265625,1283429428883663190972186961851609375
%N a(n) = ((4*n)!! - (4*n-1)!!)/(4*n+1).
%C Sequence is inspired by A273889. The same argument in A273889 can be used here to prove the expression evaluates to integers.
%H Chai Wah Wu, <a href="/A273983/b273983.txt">Table of n, a(n) for n = 1..202</a>
%o (Python)
%o doublefac=lambda x:1 if x<2 else x*doublefac(x-2)
%o for i in range(200):
%o print(i,(doublefac(4*i)-doublefac(4*i-1))//(4*i+1))
%o # _Brian Cheung_, Jun 15 2016
%Y Cf. A273889, A007912.
%K nonn
%O 1,2
%A _Chai Wah Wu_, Jun 05 2016
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