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 A146752 #14 Sep 24 2022 02:21:49
%S A146752 1,7,71,1159,5197,148025,730141,29616293,125438657,1319937329,
%T A146752 77390680651,76972298827,319946679037,3504590799071,289784158718029,
%U A146752 25703039917515461,1114069690728835,112203290640603311
%N A146752 a(n) = numerator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
%C A146752 Previous name was: a(n) is the numerator of k_n such that Integral_{x=0..1} ((1+x^(3n))/sqrt(1-x^3)) dx = k_n*Gamma(1/3)^3/(2^(1/3)*sqrt(3)*Pi) for n >= 0.
%C A146752 General formula: Integral_{x=0..1} ((1+x^(3n))/sqrt(1-x^3)) dx = G_3 * k_n = G_3*A146752(n)/A146753(n) = A118292*A146752(n)/A146753(n) where G_3 = (Gamma(1/3)^3)/(2^(1/3)*sqrt(3)*Pi).
%F A146752 a(n) = numerator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
%t A146752 Table[Numerator[(1/2) (1 + Product[(2 (1 + 3 k))/(5 + 6 k), {k, 0, n - 1}])], {n, 0, 30}]
%Y A146752 Cf. A146753 (denominator), A118292 (G_3).
%K A146752 nonn,frac
%O A146752 0,2
%A A146752 _Artur Jasinski_, Nov 01 2008
%E A146752 Simpler name (using given formula) from _Joerg Arndt_, Sep 24 2022