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 A174123 #28 Jan 12 2025 15:56:57
%S A174123 1,4,19,112,751,5404,40573,313408,2471167,19791004,160459069,
%T A174123 1313922064,10847561089,90174127684,754009158019,6336733626112,
%U A174123 53489159252671,453258909448636,3854034482891725,32871004555812112,281127047928811201,2410285909684370788
%N A174123 Partial sums of A002893.
%H A174123 Tewodros Amdeberhan and Roberto Tauraso, <a href="http://arxiv.org/abs/1607.02483">Two triple binomial sum supercongruences</a>, arXiv:1607.02483 [math.NT], Jul 08 2016.
%F A174123 a(n) = Sum_{i=0..n} A002893(i).
%F A174123 From _Sergey Perepechko_, Feb 16 2011: (Start)
%F A174123 O.g.f.: 2*sqrt(2)/Pi/(1-z)/sqrt(1-6*z-3*z^2+sqrt((1-z)^3*(1-9*z)))* EllipticK(8*z^(3/2)/(1-6*z-3*z^2+sqrt((1-z)^3*(1-9*z)))).
%F A174123 9*(n+2)^2*a(n) - (99+86*n+19*n^2)*a(n+1) + (72+56*n+11*n^2)*a(n+2) - (n+3)^2*a(n+3)=0. (End)
%F A174123 a(n) ~ 3^(2*n + 7/2) / (32*Pi*n). - _Vaclav Kotesovec_, Jul 11 2016
%t A174123 Accumulate[Table[Sum[Binomial[n,k]^2 Binomial[2k,k],{k,0,n}],{n,0,20}]] (* _Harvey P. Dale_, May 05 2013 *)
%o A174123 (PARI) a(n)=sum(m=0,n,sum(k=0,m,binomial(m,k)^2*binomial(2*k,k)))
%Y A174123 Cf. A002893, A000172, A002895, A000984, A207321.
%K A174123 easy,nonn
%O A174123 0,2
%A A174123 _Jonathan Vos Post_, Mar 08 2010