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 A218689 #11 Sep 12 2015 11:00:28
%S A218689 1,65,93313,795985985,8178690000001,93706344780048065,
%T A218689 1453730786373283012225,26552497154713885161031745,
%U A218689 513912636558068387176582890625,10769375530849394271690330588432065,243282405272735566295972089793676717313,5763401688773271719278313934033057270226625
%N A218689 Sum_{k=0..n} C(n,k)^6*C(n+k,k)^6.
%H A218689 Vincenzo Librandi, <a href="/A218689/b218689.txt">Table of n, a(n) for n = 0..200</a>
%H A218689 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 A218689 a(n) ~ (1+sqrt(2))^(6*(2n+1))/(2^(17/4)*(Pi*n)^(11/2)*sqrt(3))
%F A218689 Generally, Sum_{k=0..n} C(n,k)^p*C(n+k,k)^p is asymptotic to (1+sqrt(2))^(p*(2*n+1))/(2^(p/2+3/4)*(Pi*n)^(p-1/2)*sqrt(p)) * (1-(2*p-1)/(4*n)+(4*p^2+24*p-19)*sqrt(2)/(96*p*n))
%t A218689 Table[Sum[Binomial[n,k]^6*Binomial[n+k,k]^6,{k,0,n}],{n,0,20}]
%Y A218689 Cf. A001850 (p=1), A005259 (p=2), A092813 (p=3), A092814 (p=4), A092815 (p=5).
%K A218689 nonn
%O A218689 0,2
%A A218689 _Vaclav Kotesovec_, Nov 04 2012