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.
%I A178078 #9 Jun 14 2023 17:13:07
%S A178078 1,0,1,1,4,12,42,147,527,1914,7039,26159,98110,370919,1412211,5410273,
%T A178078 20841886,80685792,313747624,1224895416,4799435482,18867423751,
%U A178078 74394859297,294152650731,1166021396660,4632969618849,18448290723435
%N A178078 Sequence with a (1,-1) Somos-4 Hankel transform.
%C A178078 Hankel transform is A178079.
%H A178078 G. C. Greubel, <a href="/A178078/b178078.txt">Table of n, a(n) for n = 0..1000</a>
%H A178078 Paul Barry, <a href="https://arxiv.org/abs/2306.05025">Integer sequences from elliptic curves</a>, arXiv:2306.05025 [math.NT], 2023.
%F A178078 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-2*k-i)*3^(n-2*k-i)*(-2)^i*1^(k-i) ).
%t A178078 Table[Sum[(Binomial[n-k, k]/(n-2*k+1))*Sum[Binomial[k, j]*Binomial[n-k-j-1, n-2*k-j]*3^(n-2*k-j)*(-2)^j*1^(k-j), {j, 0, k}], {k, 0, Floor[n/2]}] + ((1 + (-1)^n)*(2/3)^(n/2))/2, {n, 0, 50}] (* _G. C. Greubel_, Sep 18 2018 *)
%o A178078 (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)*3^(n-2*k-j)*(-2)^j));
%o A178078 for(n=0,50, print1(a(n), ", ")) \\ _G. C. Greubel_, Sep 18 2018
%K A178078 easy,nonn
%O A178078 0,5
%A A178078 _Paul Barry_, May 19 2010