A168432 a(n) = n^5*(n^7 + 1)/2.

0, 1, 2064, 265842, 8389120, 122071875, 1088395056, 6920652004, 34359754752, 141214797765, 500000050000, 1569214268886, 4458050348544, 11649042746887, 28346956456560, 64873169325000, 140737488879616, 291311119324809

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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A168351.

Programs

Magma

[n^5*(n^7+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Table[n^5*(n^7 + 1)/2, {n,0,30}] (* G. C. Greubel, Jul 22 2016 *)
CoefficientList[Series[x (1 +2051 x +239088 x^2 +5093880 x^3 [phone] x^4 + 81255702 x^5 [phone] x^6 [phone] x^7 +5093805 x^8 +239183 x^9 +2032 x^10)/(1-x)^13, {x,0,30}], x] (* Vincenzo Librandi, Jul 23 2016 *)

SageMath

def A168432(n): return n^5*(n^7+1)//2
print(A168432(n) for n in range(31)) # G. C. Greubel, Mar 20 2025

Formula

G.f.: x*(1 + 2051*x + 239088*x^2 + 5093880*x^3 + 33159402*x^4 + 81255702*x^5 + 81256584*x^6 + 33159072*x^7 + 5093805*x^8 + 239183*x^9 + 2032*x^10)/(1-x)^13. - Vincenzo Librandi, Jul 23 2016

E.g.f.: (1/2)*x*(2 + 2062*x + 86551*x^2 + 611511*x^3 + 1379401*x^4 + 1323652*x^5 + 627396*x^6 + 159027*x^7 + 22275*x^8 + 1705*x^9 + 66*x^10 + x^11)*exp(x). - G. C. Greubel, Mar 20 2025