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 A054339 #33 Mar 27 2022 03:52:44
%S A054339 1,36,720,10560,126720,1317888,12300288,105431040,843448320,
%T A054339 6372720640,45883588608,317013884928,2113425899520,13655982735360,
%U A054339 85837605765120,526470648692736,3158823892156416,18581317012684800,107358720517734400,610249569258700800
%N A054339 9-fold convolution of A000302 (powers of 4).
%H A054339 Vincenzo Librandi, <a href="/A054339/b054339.txt">Table of n, a(n) for n = 0..100</a>
%H A054339 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (36,-576,5376,-32256,129024,-344064,589824,-589824,262144).
%F A054339 a(n) = binomial(n+8, 8)*4^n.
%F A054339 G.f.: 1/(1-4*x)^9.
%F A054339 a(n) = A054335(n+17, 17).
%F A054339 a(n) = 36*a(n-1) - 576*a(n-2) + 5376*a(n-3) - 32256*a(n-4) + 129024*a(n-5) - 344064*a(n-6) + 589824*a(n-7) - 589824*a(n-8) + 262144*a(n-9). - _Harvey P. Dale_, Aug 30 2013
%F A054339 E.g.f.: (16/7!)*(315 + 10080*x + 70560*x^2 + 188160*x^3 + 235200*x^4 + 150528*x^5 + 50176*x^6 + 8192*x^7 + 512*x^8)*exp(4*x). - _G. C. Greubel_, Jul 21 2019
%F A054339 From _Amiram Eldar_, Mar 27 2022: (Start)
%F A054339 Sum_{n>=0} 1/a(n) = 704696/35 - 69984*log(4/3).
%F A054339 Sum_{n>=0} (-1)^n/a(n) = 2500000*log(5/4) - 11715016/21. (End)
%p A054339 seq(binomial(n+8,8)*4^n,n=0..20); # _Zerinvary Lajos_, Jun 23 2008
%t A054339 Table[Binomial[n+8,8]4^n,{n,0,20}] (* or *) LinearRecurrence[ {36,-576,5376,-32256,129024,-344064,589824,-589824,262144},{1,36,720,10560,126720,1317888,12300288,105431040,843448320},20]
%o A054339 (Magma) [Binomial(n+8, 8)*4^n: n in [0..20]]; // _Vincenzo Librandi_, May 31 2011
%o A054339 (PARI) vector(20, n, n--; 4^n*binomial(n+8, 8)) \\ _G. C. Greubel_, Jul 21 2019
%o A054339 (Sage) [4^n*binomial(n+8, 8) for n in (0..20)] # _G. C. Greubel_, Jul 21 2019
%o A054339 (GAP) List([0..20], n-> 4^n*Binomial(n+8, 8)); # _G. C. Greubel_, Jul 21 2019
%Y A054339 Cf. A000302, A054335.
%Y A054339 Cf. A038231.
%K A054339 easy,nonn
%O A054339 0,2
%A A054339 _Wolfdieter Lang_, Mar 13 2000