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 A112556 #19 Sep 08 2022 08:45:22
%S A112556 1,2,2,4,10,32,112,408,1514,5680,21472,81644,311896,1196132,4602236,
%T A112556 17757184,68680170,266200112,1033703056,4020716124,15662273840,
%U A112556 61092127492,238582873476,932758045124,3650336341240,14298633670932,56055986383412,219931273282348,863504076182884,3392593262288780,13337336618626132
%N A112556 Sums of squared terms in rows of triangle A112555.
%C A112556 First differences form A072547 and equals the unsigned central terms of triangle A112555.
%H A112556 G. C. Greubel, <a href="/A112556/b112556.txt">Table of n, a(n) for n = 0..1000</a>
%F A112556 G.f.: ( 2*(1+x)/(1-x) + x/(1-4*x)^(1/2) )/(2+x).
%F A112556 a(n) ~ 2^(2*n) / (9*sqrt(Pi*n)). - _Vaclav Kotesovec_, Mar 26 2016
%F A112556 a(n) = (1/3)*(4 - (-1/2)^n) - Sum_{j=0..n-1} binomial(2*j, j)*(-1/2)^(n-j). - _G. C. Greubel_, Jan 13 2022
%t A112556 CoefficientList[Series[(2(1+x)/(1-x)+x/(1-4x)^(1/2))/(2+x), {x,0,30}], x] (* _Harvey P. Dale_, May 26 2011 *)
%o A112556 (PARI) {a(n)=local(x=X+X*O(X^n)); polcoeff((2*(1+x)/(1-x)+x/(1-4*x)^(1/2))/(2+x),n,X)}
%o A112556 (Magma) [(1/3)*(4 - (-1/2)^n) + (n+1)*Catalan(n) - (&+[(j+1)*Catalan(j)*(-1/2)^(n-j): j in [0..n]]): n in [0..30]]; // _G. C. Greubel_, Jan 13 2022
%o A112556 (Sage) [(1/3)*(4 - (-1/2)^n) - sum( binomial(2*j, j)*(-1/2)^(n-j) for j in (0..n-1)) for n in (0..30)] # _G. C. Greubel_, Jan 13 2022
%Y A112556 Cf. A072547, A112555.
%K A112556 nonn
%O A112556 0,2
%A A112556 _Paul D. Hanna_, Sep 21 2005