A183894 Imaginary part of a Gaussian integer sequence with a Gaussian integer Somos-4 Hankel transform.

0, 1, 1, -3, -3, 25, 25, -223, -223, 2217, 2217, -23427, -23427, 258417, 258417, -2941311, -2941311, 34289041, 34289041, -407344771, -407344771, 4913508489, 4913508489, -60018592735, -60018592735, 740910077497, 740910077497, -9228860168451, -9228860168451, 115849095339489, 115849095339489

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(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

Mathematica

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 *)

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

Formula

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