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Expansion of g.f. 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-12*x)).
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%I #14 Oct 29 2023 15:27:12

%S 1,22,333,4406,55133,673566,8144701,98052262,1178225565,14146756910,

%T 169801508669,2037820760118,24454863987997,293463446955454,

%U 3521586773279037,42259168371397574,507110656046025629

%N Expansion of g.f. 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-12*x)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-151,402,-360).

%F a(n) = 22*a(n-1)-151*a(n-2)+ 402*a(n-3)- 360*a(n-4), n>3. - Harvey P. Dale, May 07 2012

%F a(n) = 96*12^n/35 +3^(n+1)/2 -2^(n+2)/15 -5^(n+3)/42. - _R. J. Mathar_, May 22 2013

%F E.g.f.: exp(2*x)*(576*exp(10*x) - 625*exp(3*x) + 315*exp(x) - 56)/210. - _Stefano Spezia_, Oct 28 2023

%t CoefficientList[Series[1/((1-2x)(1-3x)(1-5x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{22,-151,402,-360},{1,22,333,4406},30] (* _Harvey P. Dale_, May 07 2012 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_