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A244730 a(n) = 2*n^4.

%I A244730 #19 Jun 15 2025 18:29:57
%S A244730 0,2,32,162,512,1250,2592,4802,8192,13122,20000,29282,41472,57122,
%T A244730 76832,101250,131072,167042,209952,260642,320000,388962,468512,559682,
%U A244730 663552,781250,913952,1062882,1229312,1414562,1620000,1847042,2097152,2371842,2672672
%N A244730 a(n) = 2*n^4.
%H A244730 Vincenzo Librandi, <a href="/A244730/b244730.txt">Table of n, a(n) for n = 0..1000</a>
%H A244730 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A244730 G.f.: 2*(x + 11*x^2 + 11*x^3 + x^4)/(1 - x)^5.
%F A244730 a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.
%F A244730 a(n) = (A082044(n) + A099761(n+1)-2)/2. - _Bruce J. Nicholson_, Jun 12 2017
%t A244730 Table[2 n^4, {n, 0, 40}] (* or *) CoefficientList[Series[2(x + 11 x^2 + 11 x^3 + x^4)/(1 - x)^5, {x, 0, 40}], x]
%t A244730 LinearRecurrence[{5,-10,10,-5,1},{0,2,32,162,512},40] (* _Harvey P. Dale_, Jun 17 2022 *)
%o A244730 (Magma) [2*n^4: n in [0..40]];
%o A244730 (Magma) I:=[0,2,32,162, 512]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]];
%Y A244730 Cf. A000583, A141046, A219056.
%K A244730 nonn,easy
%O A244730 0,2
%A A244730 _Vincenzo Librandi_, Jul 05 2014