cp's OEIS Frontend

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.

A025966 Expansion of 1/((1-2x)(1-4x)(1-6x)(1-8x)).

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%I A025966 #13 Jul 08 2025 17:46:51
%S A025966 1,20,260,2800,27216,248640,2182720,18656000,156544256,1296655360,
%T A025966 10641146880,86744985600,703688298496,5688011079680,45855653642240,
%U A025966 368956766617600,2964331947687936,23790756829593600
%N A025966 Expansion of 1/((1-2x)(1-4x)(1-6x)(1-8x)).
%H A025966 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-140,400,-384).
%F A025966 a(n) = (2^n)*stirling2(n+4, 4), n>=0, with stirling2(n, m)=A008277(n, m).
%F A025966 a(n) = (-2^n+24*4^n-81*6^n+64*8^n)/3!.
%F A025966 G.f.: 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)).
%F A025966 E.g.f.: (-exp(2*x)+24*exp(4*x)-81*exp(6*x)+64*exp(8*x))/3!.
%t A025966 CoefficientList[Series[1/((1-2x)(1-4x)(1-6x)(1-8x)),{x,0,40}],x] (* _Harvey P. Dale_, Apr 13 2019 *)
%o A025966 (PARI) Vec(1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A025966 Fourth column of triangle A075497.
%Y A025966 Cf. A016283, A075510.
%K A025966 nonn,easy
%O A025966 0,2
%A A025966 _N. J. A. Sloane_