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 A167870 #18 Jun 06 2021 09:01:57
%S A167870 1,24,600,17600,624600,25996608,1204834752,59701593600,3086972400600,
%T A167870 164324590337600,8935798773354816,494019944564058624,
%U A167870 27678350810730366400,1567912312203901862400,89647910047704725798400
%N A167870 a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
%C A167870 The expression a(n) = B^n*Sum_{k=0..n} binomial(2*k,k)/B^k gives A006134 for B=1, A082590 (B=2), A132310 (B=3), A002457 (B=4), A144635 (B=5), A167713 (B=16).
%C A167870 The expression a(n) = B^n*Sum_{k=0..n} binomial(2*k,k)^3/B^k gives A079727 for B=1, A167867 (B=2), A167868 (B=3), A167869 (B=4), A167870 (B=16), A167871 (B=64).
%H A167870 Vincenzo Librandi, <a href="/A167870/b167870.txt">Table of n, a(n) for n = 0..200</a>
%F A167870 a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
%F A167870 Recurrence: n^3*a(n) = 8*(10*n^3 - 12*n^2 + 6*n - 1)*a(n-1) - 128*(2*n-1)^3*a(n-2). - _Vaclav Kotesovec_, Aug 13 2013
%F A167870 a(n) ~ 2^(6*n+2)/(3*(Pi*n)^(3/2)). - _Vaclav Kotesovec_, Aug 13 2013
%t A167870 Table[16^n Sum[Binomial[2k,k]^3/16^k,{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Jan 21 2012 *)
%Y A167870 Cf. A079727, A167867, A167868, A167869, A167870, A167872.
%Y A167870 Cf. A000984, A066796, A006134, A082590, A132310, A002457, A144635, A167713, A167859.
%K A167870 nonn
%O A167870 0,2
%A A167870 _Alexander Adamchuk_, Nov 14 2009
%E A167870 More terms from _Sean A. Irvine_, Apr 27 2010