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 A264447 #16 Sep 08 2022 08:46:14
%S A264447 0,110,276,510,825,1235,1755,2401,3190,4140,5270,6600,8151,9945,12005,
%T A264447 14355,17020,20026,23400,27170,31365,36015,41151,46805,53010,59800,
%U A264447 67210,75276,84035,93525,103785,114855,126776,139590,153340,168070,183825,200651,218595,237705,258030
%N A264447 a(n) = n*(n + 7)*(n + 14)*(n + 21)/24.
%C A264447 It is well-known, and easy to prove, that the product of 4 consecutive integers n*(n + 1)*(n + 2)*(n + 3) is divisible by 4!. It can be shown that the product of 4 integers in arithmetic progression n*(n + r)*(n + 2*r)*(n + 3*r) is divisible by 4! if and only if r is not divisible by 2 or 3 (see A007310 for these numbers). This is the case r = 7.
%H A264447 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A264447 O.g.f.: x*(110 - 274*x + 230*x^2 - 65*x^3)/(1 - x)^5.
%F A264447 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4. - _Vincenzo Librandi_, Nov 16 2015
%p A264447 seq( n*(n + 7)*(n + 14)*(n + 21)/24, n = 0..40 );
%t A264447 Table[n (n + 7) (n + 14) (n + 21)/24, {n, 0, 40}] (* _Vincenzo Librandi_, Nov 16 2015 *)
%t A264447 Table[Times@@(n+7*Range[0,3])/24,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,110,276,510,825},50] (* _Harvey P. Dale_, May 01 2017 *)
%o A264447 (PARI) vector(100, n, n--; n*(n+7)*(n+14)*(n+21)/24) \\ _Altug Alkan_, Nov 15 2015
%o A264447 (Magma) [n*(n+7)*(n+14)*(n+21)/24: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2015
%Y A264447 Cf. A007310, A264443, A264444, A264445, A264446, A264448, A264449, A264450.
%K A264447 nonn,easy
%O A264447 0,2
%A A264447 _Peter Bala_, Nov 13 2015