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A134631 a(n) = 5*n^5 - 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order. 2

%I #15 Jan 20 2023 16:45:24

%S 0,4,144,1152,4960,15300,38304,83104,162432,293220,497200,801504,

%T 1239264,1850212,2681280,3787200,5231104,7085124,9430992,12360640,

%U 15976800,20393604,25737184,32146272,39772800,48782500,59355504,71686944,85987552,102484260,121420800,143058304,167675904,195571332,227061520

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

%H Harvey P. Dale, <a href="/A134631/b134631.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).

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

%F G.f.: 4x*(1+30x+87x^2+32x^3)/(1-x)^6. - _R. J. Mathar_, Nov 14 2007

%e a(4)=4960 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 = 4960.

%t Table[5n^5-3n^3+2n^2,{n,0,40}] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{0,4,144,1152,4960,15300},40] (* _Harvey P. Dale_, Jan 20 2023 *)

%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, A133071.

%K nonn

%O 0,2

%A _Omar E. Pol_, Nov 04 2007

%E More terms from _Vincenzo Librandi_, Dec 14 2010

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Last modified March 28 07:46 EDT 2024. Contains 371235 sequences. (Running on oeis4.)