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 A264446 #12 Sep 08 2022 08:46:14
%S A264446 0,44,119,234,399,625,924,1309,1794,2394,3125,4004,5049,6279,7714,
%T A264446 9375,11284,13464,15939,18734,21875,25389,29304,33649,38454,43750,
%U A264446 49569,55944,62909,70499,78750,87699,97384,107844,119119,131250,144279,158249,173204,189189,206250
%N A264446 a(n) = n*(n + 5)*(n + 10)*(n + 15)/24.
%C A264446 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 = 5.
%H A264446 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A264446 O.g.f.: x*(4 - 3*x)*(7*x^2 - 17*x + 11)/(1 - x)^5.
%F A264446 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 A264446 seq( n*(n + 5)*(n + 10)*(n + 15)/24, n = 0..40 );
%t A264446 Table[n (n + 5) (n + 10) (n + 15)/24, {n, 0, 40}] (* _Vincenzo Librandi_, Nov 16 2015 *)
%o A264446 (PARI) vector(100, n, n--; n*(n+5)*(n+10)*(n+15)/24) \\ _Altug Alkan_, Nov 15 2015
%o A264446 (Magma) [n*(n+5)*(n+10)*(n+15)/24: n in [0..40]]; // _Vincenzo Librandi_, Nov 16 2015
%Y A264446 Cf. A007310, A264443, A264444, A264445, A264447, A264448, A264449, A264450.
%K A264446 nonn,easy
%O A264446 0,2
%A A264446 _Peter Bala_, Nov 13 2015