A183893 Real part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.

1, 1, -1, -1, 9, 9, -73, -73, 697, 697, -7161, -7161, 77457, 77457, -868881, -868881, 10016241, 10016241, -117935473, -117935473, 1412307481, 1412307481, -17148100569, -17148100569, 210619695913, 210619695913, -2612194773481, -2612194773481, 32668519882017, 32668519882017, -411515480555553

Offset: 0

Author

Paul Barry, Jan 07 2011

Keywords

• sign

Comments

Hankel transform of A183893(n)+I*A183894(n) is the (-4,-4) Somos-4 Gaussian integer sequence A183895(n)+I*A183896(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Programs

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

Mathematica

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 *)

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

Formula

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