A183893 - OEIS

%I #15 Sep 08 2022 08:45:55

%S 1,1,-1,-1,9,9,-73,-73,697,697,-7161,-7161,77457,77457,-868881,

%T -868881,10016241,10016241,-117935473,-117935473,1412307481,

%U 1412307481,-17148100569,-17148100569,210619695913,210619695913,-2612194773481,-2612194773481,32668519882017,32668519882017,-411515480555553

%N Real 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="/A183893/b183893.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Re(Sum{k=0..n, C(floor((n+k)/2),k)*I^k*A000108(k)}), I=sqrt(-1).

%t Table[Re[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(real(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(Real((&+[(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 0,5

%A _Paul Barry_, Jan 07 2011