A168364 a(n) = n^5*(n^2 + 1)/2.

0, 1, 80, 1215, 8704, 40625, 143856, 420175, 1064960, 2421009, 5050000, 9824111, 18040320, 31559905, 52975664, 85809375, 134742016, 205879265, 307054800, 448173919, 641600000, 902586321, 1249755760, 1705630895, 2297217024

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 (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A000578 (first differences of squares of triangular numbers), A357178 (of their cubes), A059977 (partial sums), A000217.

Programs

Magma

[n^5*(n^2+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 28 2011

Mathematica

Table[n^5(n^2+1)/2,{n,0,25}]  (* Harvey P. Dale, Apr 22 2011 *)
LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1},{0, 1, 80, 1215, 8704, 40625, 143856, 420175}, 50] (* G. C. Greubel, Jul 19 2016 *)

Formula

G.f.: x*(1 + 72*x + 603*x^2 + 1168*x^3 + 603*x^4 + 72*x^5 + x^6)/(1-x)^8. - Harvey P. Dale, Apr 22 2011

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - G. C. Greubel, Jul 19 2016

a(n) = A000217(n)^4 - A000217(n-1)^4. - Kelvin Voskuijl, Jan 16 2025