%I #18 Jul 27 2024 19:14:03

%S 1,24,375,4870,57321,636924,6829435,71574690,738951741,7552940824,

%T 76677389295,774826006110,7804690367761,78442179476724,

%U 787189784753955,7891278029367130,79048458617193381,791434402768644624,7920993017579067415,79256474201063865750,792890554575137156601

%N Expansion of g.f. 1/((1-3*x)*(1-4*x)*(1-7*x)*(1-10*x)).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24,-201,694,-840).

%F a(n) = (2*10^(n+3)-7^(n+4)+14*4^(n+3)-3^(n+5))/252. - _Yahia Kahloune_, Jun 07 2013

%F E.g.f.: exp(3*x)*(2000*exp(7*x) - 2401*exp(4*x) + 896*exp(x) - 243)/252. - _Stefano Spezia_, Jul 27 2024

%t CoefficientList[Series[1/((1-3x)(1-4x)(1-7x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{24,-201,694,-840},{1,24,375,4870},30] (* _Harvey P. Dale_, Oct 02 2017 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E a(18)-a(20) from _Stefano Spezia_, Jul 27 2024