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 A263134 #33 Sep 08 2022 08:46:14
%S A263134 1,5,26,146,861,5229,32361,202905,1284480,8191380,52543545,338641305,
%T A263134 2191124301,14224347181,92603307541,604342068085,3952451061076,
%U A263134 25898039418496,169977746765071,1117287239602471,7353933943361866,48461930821297546
%N A263134 a(n) = Sum_{k=0..n} binomial(3*k+1,k).
%C A263134 Primes in sequence: 5, 92603307541, 52176309488123582020412161, ...
%C A263134 a(n) is divisible by n for n = 1, 2, 8, 55, 82, 171, 210, 1060, 1141, ...
%H A263134 Bruno Berselli and G. C. Greubel, <a href="/A263134/b263134.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 form Bruno Berselli)
%F A263134 Recurrence: 2*n*(2*n + 1)*a(n) = (31*n^2 + 2*n - 3)*a(n-1) - 3*(3*n - 1)*(3*n + 1)*a(n-2). - _Vaclav Kotesovec_, Oct 11 2015
%F A263134 a(n) ~ 27^(n + 3/2)/(23*sqrt(Pi*n)*4^(n + 1)). - _Vaclav Kotesovec_, Oct 11 2015
%t A263134 Table[Sum[Binomial[3 k + 1, k], {k, 0, n}], {n, 0, 25}]
%o A263134 (Sage) [sum(binomial(3*k+1,k) for k in (0..n)) for n in (0..25)]
%o A263134 (Magma) [&+[Binomial(3*k+1,k): k in [0..n]]: n in [0..25]];
%o A263134 (Maxima) makelist(sum(binomial(3*k+1,k),k,0,n),n,0,25);
%o A263134 (PARI) a(n) = sum(k=0, n, binomial(3*k+1,k)) \\ _Colin Barker_, Oct 16 2015
%Y A263134 Partial sums of A045721.
%Y A263134 Cf. A079309: Sum_{k=0..n} binomial(2*k+1,k).
%Y A263134 Cf. A188675: Sum_{k=0..n} binomial(3*k,k).
%Y A263134 Cf. A087413: Sum_{k=0..n} binomial(3*k+2,k).
%K A263134 nonn,easy
%O A263134 0,2
%A A263134 _Bruno Berselli_, Oct 10 2015