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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.

A249996 Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).

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%I A249996 #17 Oct 11 2022 07:39:10
%S A249996 1,-1,15,-5,191,99,2455,3515,33231,74899,474695,1371435,7071871,
%T A249996 23520899,108399735,390617755,1691480111,6378762099,26676785575,
%U A249996 103221406475,423343881951,1661998662499,6742129440215,26686105001595,107591675061391,427824901526099,1718925069371655
%N A249996 Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).
%H A249996 Colin Barker, <a href="/A249996/b249996.txt">Table of n, a(n) for n = 0..1000</a>
%H A249996 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,14,24).
%F A249996 G.f.: 1 / ((1+2*x)*(1+3*x)*(1-4*x)).
%F A249996 a(n) = ( 2^(3+2*n) + (3^(3+n)-7*2^(1+n))*(-1)^n )/21. - _Colin Barker_, Dec 29 2014
%F A249996 a(n) = -a(n-1) + 14*a(n-2) + 24*a(n-3). - _Colin Barker_, Dec 29 2014
%F A249996 E.g.f.: (1/21)*(27*exp(-3*x) - 14*exp(-2*x) + 8*exp(4*x)). - _G. C. Greubel_, Oct 11 2022
%t A249996 LinearRecurrence[{-1,14,24}, {1,-1,15}, 41] (* _G. C. Greubel_, Oct 11 2022 *)
%o A249996 (PARI) Vec(1/((1+2*x)*(1+3*x)*(1-4*x)) + O(x^50)) \\ _Michel Marcus_, Dec 29 2014
%o A249996 (Magma) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21: n in [0..40]]; // _G. C. Greubel_, Oct 11 2022
%o A249996 (SageMath) [(2^(2*n+3) +(-1)^n*(3^(n+3) -7*2^(n+1)))/21 for n in range(41)] # _G. C. Greubel_, Oct 11 2022
%Y A249996 Cf. A016269: expansion of 1/((1-2*x)*(1-3*x)*(1-4*x)).
%Y A249996 Cf. A249992, A249993, A249994, A249995.
%K A249996 sign,easy
%O A249996 0,3
%A A249996 _Alex Ratushnyak_, Dec 28 2014