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 A100515 #8 Mar 31 2023 02:53:45
%S A100515 1,1,20,42,4620,5005,2042040,1763580,59491432,95611230,776363187600,
%T A100515 235953517800,24067258815600,143627189706,12170010541088400,
%U A100515 34128942604356600,245138783756209200,1103648327722933300,497725329469811592240,94396183175309095080,538372898043179538939600
%N A100515 Denominator of Sum_{k=0..n} 1/C(3*n, 3*k).
%D A100515 M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM Review, SIAM, 1990; see pp. 126-127.
%H A100515 G. C. Greubel, <a href="/A100515/b100515.txt">Table of n, a(n) for n = 0..765</a>
%F A100515 a(n) = denominator( Sum_{k=0..n} 1/binomial(3*n,3*k) ).
%F A100515 a(n) = denominator( (3*n+1)*Sum_{k=0..n} beta(3*k+1, 3*(n-k)+1) ). - _G. C. Greubel_, Mar 28 2023
%e A100515 Sum_{k=0..n} 1/binomial(3*n,3*k) = { 1, 2, 41/20, 85/42, 9287/4620, 10034/5005, 4089347/2042040, 3529889/1763580, 119042647/59491432, 191288533/95611230, 1553111566613/776363187600, ...} = A100514(n)/a(n).
%t A100515 Table[Denominator[(3*n+1)*Sum[Beta[3k+1,3n-3k+1], {k,0,n}]], {n,0,40}] (* _G. C. Greubel_, Mar 28 2023 *)
%o A100515 (Magma) [Denominator((&+[1/Binomial(3*n, 3*k): k in [0..n]])): n in [0..40]]; // _G. C. Greubel_, Mar 28 2023
%o A100515 (SageMath)
%o A100515 def A100515(n): return denominator((3*n+1)*sum(beta(3*k+1, 3*n-3*k+1) for k in range(n+1)))
%o A100515 [A100515(n) for n in range(40)] # _G. C. Greubel_, Mar 28 2023
%Y A100515 Cf. A046825, A100513, A100514.
%K A100515 nonn,frac
%O A100515 0,3
%A A100515 _N. J. A. Sloane_, Nov 25 2004