A134633 5*n^5 + 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.

0, 10, 192, 1314, 5344, 16050, 39600, 85162, 165504, 297594, 503200, 809490, 1249632, 1863394, 2697744, 3807450, 5255680, 7114602, 9465984, 12401794, 16024800, 20449170, 25801072, 32219274, 39855744, 48876250, 59460960, 71805042, 86119264, 102630594, 121582800, 143237050, 167872512, 195786954, 227297344

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Formula

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

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

a(0)=0, a(1)=10, a(2)=192, a(3)=1314, a(4)=5344, a(5)=16050, 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, Apr 25 2012

Example

a(4)=5344 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=5344.

Maple

A134633:=n->5*n^5 + 3*n^3 + 2*n^2; seq(A134633(n), n=0..50); # Wesley Ivan Hurt, May 21 2014

Mathematica

Table[5n^5+3n^3+2n^2, {n, 0, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {0, 10, 192, 1314, 5344, 16050}, 40] (* Harvey P. Dale, Apr 25 2012 *)
CoefficientList[Series[2 x (5 + 66 x + 156 x^2 + 70 x^3 + 3x^4)/(1 - x)^6, {x, 0, 50}], x] (* Vincenzo Librandi, May 21 2014 *)

Prog

(Magma)[5*n^5+3*n^3+2*n^2: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010

Crossrefs

Cf. A000290, A000578, A000584, A045991, A100019, A133073.

Sequence in context: A072387 A356495 A244385 * A006436 A252974 A341503

Adjacent sequences: A134630 A134631 A134632 * A134634 A134635 A134636

Keyword

nonn,easy

Author

Omar E. Pol, Nov 04 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

Status

approved