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%I #14 Sep 08 2022 08:45:11
%S 0,1,20,111,328,725,1356,2275,3536,5193,7300,9911,13080,16861,21308,
%T 26475,32416,39185,46836,55423,65000,75621,87340,100211,114288,129625,
%U 146276,164295,183736,204653,227100,251131,276800,304161,333268,364175
%N a(n) = 9*n^3 - 18*n^2 + 10*n.
%C Binomial transform is A086604.
%C Second binomial transform is 3^(n-1)*n^3 = A086603(n).
%H G. C. Greubel, <a href="/A086605/b086605.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F G.f.: x*(1 + 16*x + 37*x^2)/(1-x)^4.
%F a(0)=0, a(1)=1, a(2)=20, a(3)=111, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - _Harvey P. Dale_, Mar 05 2013
%F E.g.f.: x*(1 + 9*x + 9*x^2)*exp(x). - _G. C. Greubel_, Feb 08 2020
%p seq( 9*n^3 - 18*n^2 + 10*n, n=0..40); # _G. C. Greubel_, Feb 08 2020
%t Table[9n^3-18n^2+10n,{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,1,20,111},40] (* _Harvey P. Dale_, Mar 05 2013 *)
%o (PARI) vector(41, n, my(m=n-1); 9*m^3 - 18*m^2 + 10*m) \\ _G. C. Greubel_, Feb 08 2020
%o (Magma) [9*n^3 - 18*n^2 + 10*n: n in [0..40]]; // _G. C. Greubel_, Feb 08 2020
%o (Sage) [9*n^3 - 18*n^2 + 10*n for n in (0..40)] # _G. C. Greubel_, Feb 08 2020
%o (GAP) List([0..40], n-> n*(1 + 9*(n-1)^2) ); # _G. C. Greubel_, Feb 08 2020
%Y Cf. A086603, A086604.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jul 23 2003
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