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%I #14 Sep 08 2022 08:45:55
%S 0,1,1,-3,-3,25,25,-223,-223,2217,2217,-23427,-23427,258417,258417,
%T -2941311,-2941311,34289041,34289041,-407344771,-407344771,4913508489,
%U 4913508489,-60018592735,-60018592735,740910077497,740910077497,-9228860168451,-9228860168451,115849095339489,115849095339489
%N Imaginary part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.
%C Hankel transform of A183893(n)+I*A183894(n) is the (-4,-4) Somos-4 Gaussian integer sequence A183895(n)+I*A183896(n).
%H G. C. Greubel, <a href="/A183894/b183894.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = Im(Sum{k=0..n, C(floor((n+k)/2),k)*I^k*A000108(k)}), I=sqrt(-1).
%t Table[Im[Sum[I^k*Binomial[2*k, k]*Binomial[Floor[(n + k)/2], k]/(k + 1), {k, 0, n}]], {n, 0, 50}] (* _G. C. Greubel_, Feb 21 2018 *)
%o (PARI) for(n=0,50, print1(imag(sum(k=0,n, I^k*binomial(2*k,k)* binomial( floor((n+k)/2),k)/(k+1) )), ", ")) \\ _G. C. Greubel_, Feb 21 2018
%o (Magma) [Round(Imaginary((&+[(Sqrt(-1))^k*Binomial(2*k,k)*Binomial( Floor((n+k)/2),k)/(k+1): k in [0..n]]))): n in [0..30]]; // _G. C. Greubel_, Feb 21 2018
%K sign
%O 0,4
%A _Paul Barry_, Jan 07 2011
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