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 A370912 #25 Oct 03 2024 08:19:40
%S A370912 0,15,48,105,192,315,480,693,960,1287,1680,2145,2688,3315,4032,4845,
%T A370912 5760,6783,7920,9177,10560,12075,13728,15525,17472,19575,21840,24273,
%U A370912 26880,29667,32640,35805,39168,42735,46512,50505,54720,59163,63840,68757,73920
%N A370912 a(n) = n*(n + 2)*(n + 4).
%H A370912 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A370912 a(n) = 8*Pochhammer(n/2, 3).
%F A370912 a(n) = [x^n] 3*x*(x^2 - 4*x + 5)/(x - 1)^4.
%F A370912 a(n) = 3 * A077415(n + 2).
%F A370912 From _Klaus Purath_, Aug 02 2024: (Start)
%F A370912 a(n)^2 = A028347(n+2)^3 + 4*A028347(n+2)^2.
%F A370912 a(n+1) - a(n) = A211441(n+2).
%F A370912 a(n) = 3*Sum_{i = 1..n} A028387(i). (End)
%F A370912 E.g.f.: exp(x)*x*(15 + 9*x + x^2). - _Stefano Spezia_, Aug 18 2024
%F A370912 From _Amiram Eldar_, Oct 03 2024: (Start)
%F A370912 Sum_{n>=1} 1/a(n) = 11/96.
%F A370912 Sum_{n>=1} (-1)^(n+1)/a(n) = 5/96. (End)
%p A370912 a := n -> n*(n + 2)*(n + 4): seq(a(n), n = 0..40);
%p A370912 # Using the generating function:
%p A370912 gf := 3*x*(x^2 - 4*x + 5)/(x - 1)^4: ser := series(gf, x, 42):
%p A370912 seq(coeff(ser, x, n), n = 0..40);
%t A370912 Table[n(n+2)(n+4), {n,0,40}] (* or *) CoefficientList[Series[3*x*(x^2 - 4*x + 5)/(x - 1)^4,{x,0,40}],x] (* _James C. McMahon_, Mar 05 2024 *)
%Y A370912 Cases of A370419(n, k): A000012 (n=0), A001477 (n=1), A005563 (n=2), this sequence (n=3), A190577(n=4).
%Y A370912 Cf. A077415, A370890.
%Y A370912 Cf. A028347, A028387, A211441.
%K A370912 nonn,easy
%O A370912 0,2
%A A370912 _Peter Luschny_, Mar 05 2024