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 A108476 #18 Jan 20 2025 03:59:07
%S A108476 1,2,24,160,1232,9120,68224,508928,3799296,28357120,211662848,
%T A108476 1579868160,11792306176,88018952192,656982441984,4903783628800,
%U A108476 36602339459072,273203580764160,2039219289063424,15220939987877888
%N A108476 Expansion of (1-4*x)/(1-6*x-12*x^2+8*x^3).
%C A108476 In general, Sum_{k=0..n} Sum_{j=0..n} C(2*(n-k), j)*C(2*k, j)*r^j has expansion (1 - (r+1)*x)/(1 - (r+3)*x - (r-1)*(r+3)*x^2 + (r-1)^3*x^3).
%H A108476 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,12,-8).
%F A108476 G.f.: (1-4*x)/((1+2*x)*(1-8*x+4*x^2)).
%F A108476 a(n) = 6*a(n-1)+12*a(n-2)-8*a(n-3).
%F A108476 a(n) = Sum_{k=0..n} Sum_{j=0..n} C(2*(n-k), j)*C(2*k, j)*3^j.
%F A108476 Conjecture: a(n) = A002605(n+1)*A026150(n). - _R. J. Mathar_, Jul 08 2009
%F A108476 a(0)=1, a(1)=2, a(2)=24, a(n)=6*a(n-1)+12*a(n-2)-8*a(n-3). - _Harvey P. Dale_, Feb 21 2012
%F A108476 a(n) = (-2)^n/2 +A102591(n)/2. - _R. J. Mathar_, Sep 20 2012
%t A108476 CoefficientList[Series[(1-4x)/(1-6x-12x^2+8x^3),{x,0,30}],x] (* or *) LinearRecurrence[{6,12,-8},{1,2,24},30] (* _Harvey P. Dale_, Feb 21 2012 *)
%K A108476 easy,nonn
%O A108476 0,2
%A A108476 _Paul Barry_, Jun 04 2005