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

0, 4, 144, 1152, 4960, 15300, 38304, 83104, 162432, 293220, 497200, 801504, 1239264, 1850212, 2681280, 3787200, 5231104, 7085124, 9430992, 12360640, 15976800, 20393604, 25737184, 32146272, 39772800, 48782500, 59355504, 71686944, 85987552, 102484260, 121420800, 143058304, 167675904, 195571332, 227061520

Offset: 0

Author

Omar E. Pol, Nov 04 2007

Keywords

• nonn

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A000290, A000578, A000584, A045991, A100019, A133071.

Programs

Magma

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

Mathematica

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 *)

Formula

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

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

Extensions

More terms from Vincenzo Librandi, Dec 14 2010