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%I #19 Feb 15 2017 02:55:36
%S 1,3,14,68,326,1532,7068,32104,143942,638444,2806196,12239768,
%T 53035804,228504408,979640696,4181649360,17780949574,75348050252,
%U 318312780612,1341015321784,5635404667700,23628002057736,98861122208008,412853709749168,1721097463947036
%N a(n) = 4^n*(n/4 + binomial(n-1/2, -1/2)).
%H G. C. Greubel, <a href="/A241478/b241478.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..200 from Vincenzo Librandi)
%F a(n) = 4^n*(n/4 + Gamma(n+1/2)/(sqrt(Pi)*Gamma(n+1))).
%F G.f.: x/(1 - 4*x)^2 + 1/sqrt(1 - 4*x). - _Ilya Gutkovskiy_, Feb 15 2017
%p A241478 := n -> 4^n*(n/4+GAMMA(n+1/2)/(sqrt(Pi)*GAMMA(n+1))); seq(A241478(n), n=0..24);
%t Table[4^n (n/4 + Binomial[n - 1/2, -1/2]), {n, 0, 40}] (* _Vincenzo Librandi_, Apr 25 2014 *)
%o (PARI) for(n=0,25, print1(round(4^n*(n/4 + gamma(n+1/2)/(sqrt(Pi)*gamma(n+1)))), ", ")) \\ _G. C. Greubel_, Feb 14 2017
%Y Cf. A241524.
%K nonn
%O 0,2
%A _Peter Luschny_, Apr 24 2014
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