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Expansion of 1/((1-7x)(1-8x)(1-10x)(1-12x)).
1

%I #15 Sep 05 2022 19:18:27

%S 1,37,863,16241,269703,4129041,59748151,829986817,11183795975,

%T 147236359985,1903757010519,24269169222753,305923748441767,

%U 3821741982426769,47397910610955767,584393237595955649

%N Expansion of 1/((1-7x)(1-8x)(1-10x)(1-12x)).

%H Vincenzo Librandi, <a href="/A028223/b028223.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (37, -506, 3032, -6720).

%F G.f.: 1/((1-7*x)*(1-8*x)*(1-10*x)*(1-12*x)).

%F a(n) = (3*12^(n+3)-10^(n+4)+15*8^(n+3)-8*7^(n+3))/120. [_Yahia Kahloune_, Jun 12 2013]

%F a(0)=1, a(1)=37, a(2)=863, a(3)=16241, a(n) = 37*a(n-1)-506*a(n-2)+ 3032*a(n-3)- 6720*a(n-4). - _Harvey P. Dale_, Apr 08 2014

%t CoefficientList[Series[1/((1-7x)(1-8x)(1-10x)(1-12x)),{x,0,20}],x] (* or *) LinearRecurrence[{37,-506,3032,-6720},{1,37,863,16241},20] (* _Harvey P. Dale_, Apr 08 2014 *)

%K nonn

%O 0,2

%A _N. J. A. Sloane_.