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%I A016853 #21 Dec 27 2021 22:20:36
%S A016853 0,3125,100000,759375,3200000,9765625,24300000,52521875,102400000,
%T A016853 184528125,312500000,503284375,777600000,1160290625,1680700000,
%U A016853 2373046875,3276800000,4437053125,5904900000,7737809375,10000000000,12762815625,16105100000,20113571875,24883200000
%N A016853 a(n) = (5*n)^5.
%C A016853 a(n) = A155955(n,5) for n > 4. - _Reinhard Zumkeller_, Jan 31 2009
%H A016853 Vincenzo Librandi, <a href="/A016853/b016853.txt">Table of n, a(n) for n = 0..1000</a>
%H A016853 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F A016853 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), with a(0) = 0, a(1) = 3125, a(2) = 100000, a(3) = 759375, a(4) = 3200000, a(5) = 9765625. - _Harvey P. Dale_, Jul 11 2015
%F A016853 a(n) = 3125*A000584(n). - _Michel Marcus_, Oct 24 2017
%F A016853 G.f.: 3125*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^6. - _Vincenzo Librandi_, Oct 24 2017
%t A016853 (5 Range[0, 20])^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3125, 100000, 759375, 3200000, 9765625}, 20] (* _Harvey P. Dale_, Jul 11 2015 *)
%t A016853 CoefficientList[Series[3125 x (1 + 26 x + 66 x^2 + 26 x^3 + x^4) / (1-x)^6, {x, 0, 33}], x] (* _Vincenzo Librandi_, Oct 24 2017 *)
%Y A016853 Cf. A000584.
%K A016853 nonn,easy
%O A016853 0,2
%A A016853 _N. J. A. Sloane_

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