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%I A153511 #12 Aug 25 2016 17:34:38
%S A153511 4,32,512,12288,393216,15728640,754974720,42278584320,2705829396480,
%T A153511 194819716546560,15585577323724800,1371530804487782400,
%U A153511 131666957230827110400,13693363552006019481600
%N A153511 a(n) = 4 * A051189(n).
%C A153511 A binomial sequence that produces Pi: 1/Pi= Binomial[2*n+1,n+1/2]/(2*n+1)!!
%H A153511 G. C. Greubel, <a href="/A153511/b153511.txt">Table of n, a(n) for n = 0..100</a>
%F A153511 a(n) = 4 * A051189(n).
%F A153511 From _Ilya Gutkovskiy_, Aug 22 2016: (Start)
%F A153511 E.g.f.: 4/(1 - 8*x).
%F A153511 a(n) ~ sqrt(Pi)*2^(3*n+5/2)*n^(n+1/2)/exp(n). (End)
%t A153511 Table[(2*n + 1)!!*Pi*Gamma[2*n + 2]/(Gamma[n + 3/2]^2), {n, 0, 20}]
%o A153511 (PARI) a(n) = 4*n!*8^n; \\ _Michel Marcus_, Aug 22 2016
%Y A153511 Cf. A051189.
%K A153511 nonn
%O A153511 0,1
%A A153511 _Roger L. Bagula_, Dec 28 2008

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