%I #15 Sep 08 2022 08:44:50
%S 1,33,697,12045,186001,2677653,36790057,489351885,6359059201,
%T 81227776773,1024237953817,12787834412925,158435642617201,
%U 1951116268675893,23912720464211977,291948566493573165,3553358170873164001,43140149525240231013,522680899336759084537
%N Expansion of 1/((1-5x)(1-6x)(1-10x)(1-12x)).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (33,-392,1980,-3600).
%F a(n) = (4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28. [_Yahia Kahloune_, Jun 04 2013]
%F G.f.: 1/((1-5x)(1-6x)(1-10x)(1-12x)).
%F a(n) = 33*a(n-1)-392*a(n-2)+1980*a(n-3)-3600*a(n-4). - _Wesley Ivan Hurt_, Mar 10 2015
%p A028178:=n->(4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28: seq(A028178(n), n=0..20); # _Wesley Ivan Hurt_, Mar 10 2015
%t CoefficientList[Series[1/((1 - 5 x) (1 - 6 x) (1 - 10 x) (1 - 12 x)), {x, 0, 20}], x]
%t LinearRecurrence[{33,-392,1980,-3600},{1,33,697,12045},20] (* _Harvey P. Dale_, Jul 26 2020 *)
%o (Magma) [(4*12^(n+2)-7*10^(n+2)+7*6^(n+2)-4*5^(n+2))/28 : n in [0..20]]; // _Wesley Ivan Hurt_, Mar 10 2015
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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