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A134630 a(n) = 5*n^5 - 3*n^3 - 2*n^2.

%I A134630 #23 Nov 05 2024 18:56:22
%S A134630 0,0,128,1116,4896,15200,38160,82908,162176,292896,496800,801020,
%T A134630 1238688,1849536,2680496,3786300,5230080,7083968,9429696,12359196,
%U A134630 15975200,20391840,25735248,32144156,39770496,48780000,59352800,71684028,85984416,102480896,121417200,143054460,167671808,195566976,227056896
%N A134630 a(n) = 5*n^5 - 3*n^3 - 2*n^2.
%C A134630 Coefficients and exponents are the first three prime numbers in decreasing order.
%H A134630 Vincenzo Librandi, <a href="/A134630/b134630.txt">Table of n, a(n) for n = 0..1000</a>
%H A134630 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F A134630 a(n) = 5*n^5 - 3*n^3 - 2*n^2.
%F A134630 G.f.: 4*x^2*(32+87*x+30*x^2+x^3)/(-1+x)^6. - _R. J. Mathar_, Nov 14 2007
%F A134630 a(0)=0, a(1)=0, a(2)=128, a(3)=1116, a(4)=4896, a(5)=15200, 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). - _Harvey P. Dale_, Jun 01 2014
%e A134630 a(4)=4896 because 4^5=1024, 5*1024=5120, 4^3=64, 3*64=192, 4^2=16, 2*16=32 and we can write 5120-192-32=4896.
%p A134630 A134630:=n->5*n^5 - 3*n^3 - 2*n^2; seq(A134630(n), n=0..50); # _Wesley Ivan Hurt_, May 21 2014
%t A134630 CoefficientList[Series[4 x^2 (32 + 87 x + 30 x^2 + x^3)/(-1 + x)^6, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 21 2014 *)
%t A134630 Table[5n^5-3n^3-2n^2,{n,0,40}] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,0,128,1116,4896,15200},40] (* _Harvey P. Dale_, Jun 01 2014 *)
%o A134630 (Magma)[5*n^5-3*n^3 -2*n^2: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010
%Y A134630 Cf. A000290, A000578, A000584, A045991, A100019, A133070.
%K A134630 nonn,easy
%O A134630 0,3
%A A134630 _Omar E. Pol_, Nov 04 2007
%E A134630 More terms from _Vincenzo Librandi_, Dec 14 2010