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 A370914 #15 Oct 03 2024 08:31:24
%S A370914 0,45,120,231,384,585,840,1155,1536,1989,2520,3135,3840,4641,5544,
%T A370914 6555,7680,8925,10296,11799,13440,15225,17160,19251,21504,23925,26520,
%U A370914 29295,32256,35409,38760,42315,46080,50061,54264,58695,63360,68265,73416,78819,84480
%N A370914 a(n) = n * (n + 4) * (n + 8).
%H A370914 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A370914 a(n) = 64*Pochhammer(n/4, 3).
%F A370914 a(n) = n^3 + 12*n^2 + 32*n.
%F A370914 a(n) = [x^n] 3*x*(7*x^2 - 20*x + 15)/(x - 1)^4.
%F A370914 a(n) = Sum_{k=0..3} Stirling1(3, k)*(-4)^(3 - k)*n^k.
%F A370914 From _Amiram Eldar_, Oct 03 2024: (Start)
%F A370914 Sum_{n>=1} 1/a(n) = 1217/26880.
%F A370914 Sum_{n>=1} (-1)^(n+1)/a(n) = 149/8960. (End)
%p A370914 a := n -> n * (n + 4) * (n + 8): seq(a(n), n = 0..40);
%t A370914 LinearRecurrence[{4, -6, 4, -1}, {0, 45, 120, 231}, 41] (* _Hugo Pfoertner_, Mar 06 2024 *)
%Y A370914 Cf. A370915 (case n=3).
%K A370914 nonn,easy
%O A370914 0,2
%A A370914 _Peter Luschny_, Mar 06 2024