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 A100516 #10 Jun 24 2022 19:51:41
%S A100516 1,2,9,20,155,21,7441,3224,5697,3575,28523,27183,70357417,4661447,
%T A100516 386395,8959408,10028928779,525966759,1476346738309,35051863075,
%U A100516 847581175,709068173,62385202783,20340152122,119483756745025,4418168441921,311960929172031
%N A100516 Numerator of Sum_{k=0..n} 1/binomial(n,k)^2.
%D A100516 H. W. Gould, Combinatorial Identities, Morgantown, 1972, p. 50, formula (5.2).
%H A100516 G. C. Greubel, <a href="/A100516/b100516.txt">Table of n, a(n) for n = 0..1000</a>
%F A100516 a(n) = numerator( 3*(n+1)^2/((n+2)*(2*n+3)*Catalan(n+1)) * Sum_{k=1..n+1} binomial(2*k, k)/k ). - _G. C. Greubel_, Jun 24 2022
%e A100516 1, 2, 9/4, 20/9, 155/72, 21/10, 7441/3600, 3224/1575, 5697/2800, 3575/1764, 28523/14112, 27183/13475, 70357417/34927200, 4661447/2316600, ... = A100516/A100517
%t A100516 Table[3*(n+1)^2/((n+2)*(2*n+3)*CatalanNumber[n+1])*Sum[((k+ 1)/k)*CatalanNumber[k], {k,n+1}], {n,0,40}]//Numerator (* _G. C. Greubel_, Jun 24 2022 *)
%o A100516 (Magma) [Numerator( (&+[1/Binomial(n,k)^2: k in [0..n]]) ): n in [0..40]]; // _G. C. Greubel_, Jun 24 2022
%o A100516 (SageMath) [numerator(sum(1/binomial(n,k)^2 for k in (0..n))) for n in (0..40)] # _G. C. Greubel_, Jun 24 2022
%o A100516 (PARI) a(n) = numerator(sum(k=0, n, 1/binomial(n,k)^2)); \\ _Michel Marcus_, Jun 24 2022
%Y A100516 Cf. A000108, A046825, A100517, A100518.
%K A100516 nonn,frac
%O A100516 0,2
%A A100516 _N. J. A. Sloane_, Nov 25 2004