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 A349312 #14 Nov 15 2021 08:56:48
%S A349312 1,2,14,158,2106,30762,476406,7683926,127692530,2171184146,
%T A349312 37592376734,660522703886,11747865153962,211093333172282,
%U A349312 3826315983647366,69880933123237958,1284661783610775010,23753502514840942882,441458929706855144494,8242097867816771820926
%N A349312 G.f. A(x) satisfies: A(x) = (1 + x * A(x)^6) / (1 - x).
%H A349312 Seiichi Manyama, <a href="/A349312/b349312.txt">Table of n, a(n) for n = 0..500</a>
%F A349312 a(n) = Sum_{k=0..n} binomial(n+5*k,6*k) * binomial(6*k,k) / (5*k+1).
%F A349312 a(n) = F([(1+n)/5, (2+n)/5, (3+n)/5, (4+n)/5, 1+n/5, -n], [2/5, 3/5, 4/5, 1, 6/5], -1), where F is the generalized hypergeometric function. - _Stefano Spezia_, Nov 14 2021
%F A349312 a(n) ~ sqrt(1 + 5*r) / (2^(6/5) * 3^(7/10) * sqrt(5*Pi) * (1-r)^(3/10) * n^(3/2) * r^(n + 1/5)), where r = 0.04941755525635041337247049893940451999923592381716... is the smallest real root of the equation 5^5 * (1-r)^6 = 6^6 * r. - _Vaclav Kotesovec_, Nov 15 2021
%t A349312 nmax = 19; A[_] = 0; Do[A[x_] = (1 + x A[x]^6)/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A349312 Table[Sum[Binomial[n + 5 k, 6 k] Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 19}]
%Y A349312 Cf. A002295, A006318, A346626, A346648, A349310, A349311, A349313, A349314.
%K A349312 nonn
%O A349312 0,2
%A A349312 _Ilya Gutkovskiy_, Nov 14 2021