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%I #8 Jul 07 2021 17:10:52
%S 1,90,6156,387720,23705136,1432922400,86230132416,5179923146880,
%T 310942155338496,18660051727004160,1119687641441381376,
%U 67183287394552842240,4031045937469026349056,241863924899255181189120
%N Third column of triangle A089504.
%C Convolution of A089507 with powers of 60.
%H Harvey P. Dale, <a href="/A089513/b089513.txt">Table of n, a(n) for n = 0..562</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (90,-1944,8640).
%F G.f.: 1/((1-3*2*1*x)*(1-4*3*2*x)*(1-5*4*3*x)).
%F a(n)=A089504(n+3, 3), n>=0.
%F a(n)= (50*(5*4*3)^n - 24*(4*3*2)^n + (3*2*1)^n)/27 = (6^n)*(5*10^(n+1) - 3*2^(2*n+3) + 1)/27.
%t CoefficientList[Series[1/(1-90 x+1944 x^2-8640 x^3),{x,0,20}],x] (* or *) LinearRecurrence[{90,-1944,8640},{1,90,6156},20] (* _Harvey P. Dale_, Jul 07 2021 *)
%Y Cf. A089505, A089507, A089514.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Dec 01 2003