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 A100511 #21 Apr 03 2023 14:31:52
%S A100511 0,3,22,126,652,3190,15060,69356,313624,1398438,6166660,26948548,
%T A100511 116888232,503811516,2159864392,9216445080,39168381488,165864540934,
%U A100511 700151508324,2947120122068,12373581565960,51831196048212,216659135089496,903925011410536
%N A100511 a(n) = Sum_{j=0..n} Sum_{k=0..n} binomial(n,j)*binomial(n,k)*max(j,k).
%H A100511 G. C. Greubel, <a href="/A100511/b100511.txt">Table of n, a(n) for n = 0..1000</a>
%H A100511 M. Klamkin, ed., <a href="https://doi.org/10.1137/1.9781611971729">Problems in Applied Mathematics: Selections from SIAM Review</a>, SIAM, 1990; see pp. 127-129.
%F A100511 a(n) = n*2^(2*n-1) + (n/2)*binomial(2*n, n). [Typo corrected by _Ognjen Dragoljevic_, Dec 26 2017]
%F A100511 From _G. C. Greubel_, Apr 01 2023: (Start)
%F A100511 G.f.: x*(2 + sqrt(1-4*x))/(1-4*x)^2.
%F A100511 E.g.f.: x*(2*exp(4*x)+ exp(2*x)*(BesselI(0, 2*x) + BesselI(1, 2*x))). (End)
%t A100511 Table[n*(4^n +(n+1)*CatalanNumber[n])/2, {n,0,40}] (* _G. C. Greubel_, Apr 01 2023 *)
%o A100511 (PARI) a(n) = n*2^(2*n-1) + (n/2)*binomial(2*n, n); \\ _Michel Marcus_, Dec 26 2017
%o A100511 (Magma) [n*(4^n +(n+1)*Catalan(n))/2: n in [0..40]]; // _G. C. Greubel_, Apr 01 2023
%o A100511 (SageMath) [n*(4^n +binomial(2*n,n))/2 for n in range(41)] # _G. C. Greubel_, Apr 01 2023
%Y A100511 Cf. A000108, A002457, A033504.
%K A100511 nonn
%O A100511 0,2
%A A100511 _N. J. A. Sloane_, Nov 24 2004