A168527 a(n) = n^6*(n^2 + 1)/2.

0, 1, 160, 3645, 34816, 203125, 863136, 2941225, 8519680, 21789081, 50500000, 108065221, 216483840, 410278765, 741659296, 1287140625, 2155872256, 3499947505, 5526986400, 8515304461, 12832000000, 18954312741, 27494626720, 39229510585, 55133208576

Offset: 0

Author

N. J. A. Sloane, Dec 11 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A168526.

Programs

Magma

[n^6*(n^2 + 1)/2: n in [0..30]]; // Vincenzo Librandi, Jul 25 2016

Mathematica

Table[n^6*(n^2+1)/2, {n,0,40}] (* G. C. Greubel, Jul 25 2016 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {0,1,160,3645,34816,203125, 863136,2941225,8519680}, 30] (* Harvey P. Dale, May 10 2018 *)

SageMath

def A168527(n): return n^4*binomial(n^2+1,2)
print([A168527(n) for n in range(41)]) # G. C. Greubel, Mar 20 2025

Formula

G.f.: (x + 151*x^2 + 2241*x^3 + 7687*x^4 + 7687*x^5 + 2241*x^6 + 151*x^7 + x^8)/(1 - x)^9. - G. C. Greubel, Jul 25 2016

E.g.f.: (1/2)*x*(2 + 158*x + 1056*x^2 + 1766*x^3 + 1065*x^4 + 267*x^5 + 28*x^6 + x^7)*exp(x). - G. C. Greubel, Mar 20 2025