A168507 a(n) = n^5*(n^10 + 1)/2.

0, 1, 16400, 7174575, 536871424, 15258790625, 235092496176, 2373780763375, 17592186060800, 102945566076849, 500000000050000, 2088624084788351, 7703510787417600, 25592946507231025, 77784047779175024, 218946945190809375, 576460752303947776

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Crossrefs

Cf. A006003, A168351.

Programs

Magma

[n^5*(n^10+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Table[n^5*(n^10+1)/2, {n,0,30}] (* G. C. Greubel, Jul 24 2016 *)
LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{0,1,16400,7174575,536871424,15258790625,235092496176, 2373780763375,17592186060800,102945566076849,500000000050000, 2088624084788351,7703510787417600,25592946507231025,77784047779175024, 218946945190809375}, 30] (* Harvey P. Dale, Apr 25 2017 *)

SageMath

def A168507(n): return n^5*(n^10 +1)//2
print([A168507(n) for n in range(31)]) # G. C. Greubel, Mar 20 2025

Formula

G.f.: x*(1 + 16384*x + 6912295*x^2 + 424045664*x^3 + 7520614661*x^4 + 51388498688*x^5 + 155693801427*x^6 + 223769405760*x^7 + 155693801427*x^8 + 51388498688*x^9 + 7520614661*x^10 + 424045664*x^11 + 6912295*x^12 + 16384*x^13 + x^14)/(1 - x)^16. - Vincenzo Librandi, Jul 24 2016

a(n) = A006003(n^5). - G. C. Greubel, Mar 20 2025