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 A218692 #11 Sep 12 2015 11:00:29
%S A218692 1,9,1945,783657,333935001,216152253009,148273286805001,
%T A218692 112444816742316585,93273051852487532953,80885382627785790555009,
%U A218692 73726153308964013326434945,69714999360408389332640853105,67921574835559806028030517001225,67965584346796032477336615843457665
%N A218692 Sum_{k=0..n} C(n,k)^6*C(n+k,k)^3.
%H A218692 Vincenzo Librandi, <a href="/A218692/b218692.txt">Table of n, a(n) for n = 0..200</a>
%H A218692 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Asymptotic of generalized Apery sequences with powers of binomial coefficients</a>, Nov 04 2012
%F A218692 a(n) ~ ((1+sqrt(5))/2)^(3*(5*n+4)-3/2)/(5^(1/4)*(2*Pi*n)^4*sqrt(3))
%F A218692 Generally, Sum_{k=0..n} C(n,k)^(2*q)*C(n+k,k)^q is asymptotic to ((1+sqrt(5))/2)^(q*(5*n+4)-3/2)/(5^(1/4)*sqrt(q*(2*Pi*n)^(3*q-1))) * (1-(25*q^2+96*q-61)/(120*q*n)-(13*q^2-36*q+17)*sqrt(5)/(60*q*n)).
%t A218692 Table[Sum[Binomial[n,k]^6*Binomial[n+k,k]^3,{k,0,n}],{n,0,20}]
%Y A218692 Cf. A005258, A218690.
%K A218692 nonn
%O A218692 0,2
%A A218692 _Vaclav Kotesovec_, Nov 04 2012