A134632 - OEIS

%I #15 Sep 08 2022 08:45:32

%S 0,6,176,1278,5280,15950,39456,84966,165248,297270,502800,809006,

%T 1249056,1862718,2696960,3806550,5254656,7113446,9464688,12400350,

%U 16023200,20447406,25799136,32217158,39853440,48873750,59458256,71802126,86116128,102627230,121579200,143233206,167868416,195782598,227292720

%N 5*n^5 + 3*n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.

%H Vincenzo Librandi, <a href="/A134632/b134632.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = 5*n^5 + 3*n^3 - 2*n^2.

%F G.f.: 2x*(3+70x+156x^2+66x^3+5x^4)/(1-x)^6. - _R. J. Mathar_, Nov 14 2007

%e a(4)=5280 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=5280.

%p A134632:=n->5*n^5 + 3*n^3 - 2*n^2; seq(A134632(n), n=0..50); # _Wesley Ivan Hurt_, May 21 2014

%t CoefficientList[Series[2 x (3 + 70 x + 156 x^2 + 66 x^3 + 5 x^4)/(1 - x)^6, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 21 2014 *)

%o (Magma)[5*n^5+3*n^3-2*n^2: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010

%Y Cf. A000290, A000578, A000584, A045991, A100019, A133072.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, Nov 04 2007

%E More terms from _Vincenzo Librandi_, Dec 14 2010