cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A178076 Sequence with a (4,-8) Somos-4 Hankel transform.

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%I A178076 #6 Sep 19 2018 08:44:56
%S A178076 1,0,2,-2,8,-20,64,-200,656,-2184,7408,-25456,88480,-310464,1098304,
%T A178076 -3912896,14026752,-50557184,183110400,-666079872,2432399104,
%U A178076 -8914099840,32772922112,-120844493056,446793362944,-1656004554752
%N A178076 Sequence with a (4,-8) Somos-4 Hankel transform.
%C A178076 Hankel transform is A178077.
%H A178076 G. C. Greubel, <a href="/A178076/b178076.txt">Table of n, a(n) for n = 0..1000</a>
%F A178076 a(n) = Sum_{k=0..floor(n/2)} ( (C(n-k,k)/(n-2k+1))*Sum_{i=0..k} C(k,i)*C(n-k-i-1,n-2k-i)*(-2)^(n-2k-i)*2^i*2^(k-i) ).
%t A178076 Table[If[n == 0, 1, Sum[(Binomial[n-k,k]/(n-2*k+1))* Sum[Binomial[k, j]*Binomial[n-k-j-1, n-2*k-j]*(-2)^(n-2*k-j)*2^k, {j, 0, k}], {k, 0, Floor[n/2]}] + (1 + (-1)^n)/2], {n, 0, 100}] (* _G. C. Greubel_, Sep 18 2018 *)
%o A178076 (PARI) a(n) = sum(k=0,floor(n/2), sum(j=0,k, (binomial(n-k,k)/(n-2*k+1)) *binomial(k,j)*binomial(n-k-j-1,n-2*k-j)*(-2)^(n-2*k-j)*2^k));
%o A178076 for(n=0,30, print1(a(n), ", ")) \\ _G. C. Greubel_, Sep 18 2018
%K A178076 easy,sign
%O A178076 0,3
%A A178076 _Paul Barry_, May 19 2010