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 A346648 #12 Nov 15 2021 08:57:11
%S A346648 1,2,9,73,751,8587,104425,1323952,17303503,231455104,3153167249,
%T A346648 43597546197,610232050453,8629733401556,123114479858631,
%U A346648 1769728635257503,25607523627970183,372688563309335806,5451995469296025115,80122698147986922194,1182341393088427774071
%N A346648 a(n) = Sum_{k=0..n} binomial(n,k) * binomial(6*k,k) / (5*k + 1).
%C A346648 Binomial transform of A002295.
%H A346648 Seiichi Manyama, <a href="/A346648/b346648.txt">Table of n, a(n) for n = 0..500</a>
%F A346648 G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x * (1 - x)^4 * A(x)^6.
%F A346648 G.f.: Sum_{k>=0} ( binomial(6*k,k) / (5*k + 1) ) * x^k / (1 - x)^(k+1).
%F A346648 a(n) ~ 49781^(n + 3/2) / (3359232 * sqrt(3*Pi) * n^(3/2) * 5^(5*n + 3/2)). - _Vaclav Kotesovec_, Jul 30 2021
%t A346648 Table[Sum[Binomial[n, k] Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 20}]
%t A346648 nmax = 20; A[_] = 0; Do[A[x_] = 1/(1 - x) + x (1 - x)^4 A[x]^6 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A346648 nmax = 20; CoefficientList[Series[Sum[(Binomial[6 k, k]/(5 k + 1)) x^k/(1 - x)^(k + 1), {k, 0, nmax}], {x, 0, nmax}], x]
%t A346648 Table[HypergeometricPFQ[{1/6, 1/3, 1/2, 2/3, 5/6, -n}, {2/5, 3/5, 4/5, 1, 6/5}, -46656/3125], {n, 0, 20}]
%o A346648 (PARI) a(n) = sum(k=0, n, binomial(n,k)*binomial(6*k,k)/(5*k + 1)); \\ _Michel Marcus_, Jul 26 2021
%Y A346648 Cf. A002295, A007317, A188687, A226910, A346646, A346647, A346649, A346650.
%K A346648 nonn
%O A346648 0,2
%A A346648 _Ilya Gutkovskiy_, Jul 26 2021