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 A091004 #23 Dec 14 2024 03:59:19
%S A091004 0,1,-2,8,-20,68,-188,596,-1724,5300,-15644,47444,-141308,425972,
%T A091004 -1273820,3829652,-11472572,34450484,-103285916,309988820,-929704316,
%U A091004 2789637236,-8367863132,25105686548,-75312865340,225946984628,-677824176668,2033506084436
%N A091004 Expansion of x*(1-x)/((1-2*x)*(1+3*x)).
%C A091004 Inverse binomial transform of A091001.
%H A091004 G. C. Greubel, <a href="/A091004/b091004.txt">Table of n, a(n) for n = 0..1000</a>
%H A091004 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,6).
%F A091004 G.f.: x*(1-x)/((1-2*x)*(1+3*x)).
%F A091004 a(n) = (3*2^n - 8*(-3)^n + 5*0^n)/30.
%F A091004 2^n = A091003(n) + 3*a(n) + 6*A091005(n).
%F A091004 a(n+1) = Sum_{k=0..n} A112555(n,k)*(-3)^k. - _Philippe Deléham_, Sep 11 2009
%F A091004 E.g.f.: (3*exp(2*x) - 8*exp(-3*x) + 5)/30. - _G. C. Greubel_, Feb 01 2019
%t A091004 CoefficientList[Series[x(1-x)/((1-2x)(1+3x)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jan 17 2017 *)
%t A091004 Join[{0}, LinearRecurrence[{-1, 6}, {1, -2}, 30]] (* _G. C. Greubel_, Feb 01 2019 *)
%o A091004 (PARI) vector(30, n, n--; (3*2^n - 8*(-3)^n + 5*0^n)/30) \\ _G. C. Greubel_, Feb 01 2019
%o A091004 (Magma) [0] cat [(3*2^n - 8*(-3)^n)/30: n in [1..30]]; // _G. C. Greubel_, Feb 01 2019
%o A091004 (Sage) [0] + [(3*2^n - 8*(-3)^n)/30 for n in (1..30)] # _G. C. Greubel_, Feb 01 2019
%o A091004 (GAP) Concatenation([0], List([1..30], n -> (3*2^n - 8*(-3)^n)/30)); # _G. C. Greubel_, Feb 01 2019
%Y A091004 Cf. A091001, A091003, A091005, A112555.
%K A091004 easy,sign
%O A091004 0,3
%A A091004 _Paul Barry_, Dec 13 2003