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 A120278 #16 Aug 31 2025 19:16:14
%S A120278 2,10,38,136,486,1760,6466,24042,90238,341190,1297574,4958114,
%T A120278 19019254,73196994,282492254,1092867904,4236849774,16455966944,
%U A120278 64020347914,249431257704,973100041934,3800867789884,14862066265434,58170868424084
%N A120278 a(n) = Sum_{m=1..n} Sum_{k=1..m} C(2*k,k), where C(2*k,k) = (2*k)!/(k!)^2 = A000984(k).
%C A120278 a(2*(p-1)) is divisible by p^2 for p=7,13,19,31,37,43,61,67.. A002476 (Primes of the form 6m + 1).
%H A120278 Vincenzo Librandi, <a href="/A120278/b120278.txt">Table of n, a(n) for n = 1..200</a>
%F A120278 a(n) = Sum_{m=1..n} Sum_{k=1..m} (2*k)!/(k!)^2.
%F A120278 a(n) = 2 * Sum_{k=1..n} A079309(k) = Sum_{k=1..n} A066796(k). - _Alexander Adamchuk_, Sep 01 2006
%F A120278 G.f.: x*(1/sqrt(1-4*x)-1)/(x*(x-1)^2). - _Harvey P. Dale_, May 24 2011
%F A120278 Recurrence: n*a(n) = 2*(3*n-1)*a(n-1) - (9*n-4)*a(n-2) + 2*(2*n-1)*a(n-3). - _Vaclav Kotesovec_, Oct 19 2012
%F A120278 a(n) ~ 2^(2*n+4)/(9*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 19 2012
%t A120278 Table[Sum[Sum[(2k)!/(k!)^2,{k,1,m}],{m,1,n}],{n,1,50}]
%t A120278 CoefficientList[Series[(1/Sqrt[1-4 x]-1)/((x-1)^2 x),{x,0,50}],x] (* _Harvey P. Dale_, May 24 2011 *)
%Y A120278 Cf. A000984, A066796, A002476.
%Y A120278 Cf. A066796, A079309.
%K A120278 nonn,changed
%O A120278 1,1
%A A120278 _Alexander Adamchuk_, Jul 04 2006