%I #11 Jul 23 2019 08:07:34
%S 1,20,260,2800,27216,248640,2182720,18656000,156544256,1296655360,
%T 10641146880,86744985600,703688298496,5688011079680,45855653642240,
%U 368956766617600,2964331947687936,23790756829593600
%N Expansion of 1/((1-2x)(1-4x)(1-6x)(1-8x)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-140,400,-384).
%F a(n) = (2^n)*stirling2(n+4, 4), n>=0, with stirling2(n, m)=A008277(n, m).
%F a(n) = (-2^n+24*4^n-81*6^n+64*8^n)/3!.
%F G.f.: 1/((1-2*x)*(1-4*x)*(1-6*x)*(1-8*x)).
%F E.g.f.: (-exp(2*x)+24*exp(4*x)-81*exp(6*x)+64*exp(8*x))/3!.
%t CoefficientList[Series[1/((1-2x)(1-4x)(1-6x)(1-8x)),{x,0,40}],x] (* _Harvey P. Dale_, Apr 13 2019 *)
%o (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 Fourth column of triangle A075497.
%Y Cf. A016283, A075510.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.