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%I #14 Jan 24 2022 17:14:15
%S 1,6,30,137,588,2415,9600,37209,141336,528049,1945800,7086555,
%T 25550547,91319973,323890062,1140985116,3995155506,13913280006,
%U 48216776266,166355744244,571636515369,1957015021744,6677155551312
%N COMPOSE triangular numbers with triangular numbers.
%H Harvey P. Dale, <a href="/A030280/b030280.txt">Table of n, a(n) for n = 1..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12, -57, 139, -195, 174, -102, 39, -9, 1).
%F G.f.: [(1-x)^6]/[(1-4x+3x^2-x^3)^3].
%F a(1)=1, a(2)=6, a(3)=30, a(4)=137, a(5)=588, a(6)=2415, a(7)=9600, a(8)=37209, a(9)=141336, a(n)=12*a(n-1)-57*a(n-2)+139*a(n-3)- 195*a(n-4)+ 174*a(n-5)-102*a(n-6)+39*a(n-7)-9*a(n-8)+a(n-9). - _Harvey P. Dale_, Jan 08 2013
%t CoefficientList[Series[((1-x)^6)/((1-4x+3x^2-x^3)^3),{x,0,30}],x] (* or *) LinearRecurrence[{12,-57,139,-195,174,-102,39,-9,1},{1,6,30,137,588,2415,9600,37209,141336},30] (* _Harvey P. Dale_, Jan 08 2013 *)
%K nonn,nice,easy
%O 1,2
%A _Christian G. Bower_
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