A168462 a(n) = n^5*(n^8 + 1)/2.

0, 1, 4112, 797283, 33554944, 610353125, 6530350896, 48444513607, 274877923328, 1270932943689, 5000000050000, 17261356152491, 53496602813952, 151437553481773, 396857386895984, 973097534559375, 2251799814209536

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 (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).

Crossrefs

Cf. A168351.

Programs

Magma

[n^5*(n^8+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Table[n^5 (n^8+1)/2,{n,0,30}] (* Harvey P. Dale, Jan 10 2013 *)

SageMath

def A168462(n): return n^5*(n^8+1)//2
print([A168462(n) for n in range(31)]) # G. C. Greubel, Mar 20 2025

Formula

From G. C. Greubel, Mar 20 2025: (Start)

G.f.: x*(1 +4098*x +739806*x^2 [phone]*x^3 [phone]*x^4 [phone]*x^5 [phone]*x^6 [phone]*x^7 [phone]*x^8 [phone]*x^9 +739806*x^10 +4098*x^11 + x^12)/(1-x)^14.

E.g.f.: (1/2)*x*(2 +4110*x +261650*x^2 +2532540*x^3 +7508502*x^4 +9321312*x^5 +5715424*x^6 +1899612*x^7 +359502*x^8 +39325*x^9 +2431*x^10 +78*x^11 +x^12)*exp(x). (End)