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 A346680 #15 Aug 05 2021 13:12:24
%S A346680 1,0,4,18,122,847,6237,47583,373149,2989111,24354777,201214021,
%T A346680 1681719343,14193619647,120800146953,1035593096367,8934344395053,
%U A346680 77510878324671,675799844685937,5918354494345863,52037647837001257,459200394617540288,4065477723321641932
%N A346680 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(4*k,k) / (3*k + 1).
%H A346680 Seiichi Manyama, <a href="/A346680/b346680.txt">Table of n, a(n) for n = 0..1000</a>
%F A346680 G.f. A(x) satisfies: A(x) = 1 / (1 + x) + x * (1 + x)^3 * A(x)^4.
%F A346680 a(n) ~ 2^(8*n + 17/2) / (283 * sqrt(Pi) * n^(3/2) * 3^(3*n + 3/2)). - _Vaclav Kotesovec_, Jul 30 2021
%F A346680 D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) -(n-1)*(229*n^2-155*n+24)*a(n-1) -8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-2)=0. - _R. J. Mathar_, Aug 05 2021
%t A346680 Table[Sum[(-1)^(n - k) Binomial[4 k, k]/(3 k + 1), {k, 0, n}], {n, 0, 22}]
%t A346680 nmax = 22; A[_] = 0; Do[A[x_] = 1/(1 + x) + x (1 + x)^3 A[x]^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%o A346680 (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(4*k, k)/(3*k + 1)); \\ _Michel Marcus_, Jul 29 2021
%Y A346680 Cf. A002293, A032357, A188678, A345367, A346664.
%Y A346680 Cf. A346681, A346682, A346683, A346684.
%K A346680 nonn
%O A346680 0,3
%A A346680 _Ilya Gutkovskiy_, Jul 29 2021