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 A011940 #30 Oct 27 2024 09:26:00 %S A011940 0,0,0,0,0,4,12,28,56,100,168,264,396,572,800,1092,1456,1904,2448, %T A011940 3100,3876,4788,5852,7084,8500,10120,11960,14040,16380,19000,21924, %U A011940 25172,28768,32736,37100,41888,47124,52836,59052,65800,73112,81016,89544,98728,108600,119196,130548,142692,155664,169500 %N A011940 a(n) = floor(n*(n-1)*(n-2)*(n-3)/30). %H A011940 Vincenzo Librandi, <a href="/A011940/b011940.txt">Table of n, a(n) for n = 0..1000</a> %H A011940 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1,1,-4,6,-4,1). %F A011940 a(n) = 4 * A011795(n). %F A011940 From _R. J. Mathar_, Apr 15 2010: (Start) %F A011940 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-5) - 4*a(n-6) + 6*a(n-7) - 4*a(n-8) + a(n-9). %F A011940 G.f.: 4*x^5*(1-x+x^2) / ((1-x)^5*(1+x+x^2+x^3+x^4) ). (End) %t A011940 CoefficientList[Series[4*x^5*(1-x+x^2)/((1-x)^4*(1-x^5)),{x,0,60}],x] (* _Vincenzo Librandi_, Jun 19 2012 *) %t A011940 LinearRecurrence[{4,-6,4,-1,1,-4,6,-4,1},{0,0,0,0,0,4,12,28,56},60] (* _Harvey P. Dale_, Nov 13 2017 *) %t A011940 Floor[4*Binomial[Range[0,60], 4]/5] (* _G. C. Greubel_, Oct 27 2024 *) %o A011940 (Magma) [Floor(n*(n-1)*(n-2)*(n-3)/30): n in [0..60]]; // _Vincenzo Librandi_, Jun 19 2012 %o A011940 (SageMath) [4*binomial(n,4)//5 for n in range(61)] # _G. C. Greubel_, Oct 27 2024 %Y A011940 Cf. A011795, A011915. %K A011940 nonn,easy %O A011940 0,6 %A A011940 _N. J. A. Sloane_