A168412 a(n) = n^5*(n^6 + 1)/2.

0, 1, 1040, 88695, 2097664, 24415625, 181402416, 988671775, 4294983680, 15690559329, 50000050000, 142655915831, 371504309760, 896080382665, 2024782853744, 4324878309375, 8796093546496, 17135948863745

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

Programs

Magma

[n^5*(n^6+1)/2: n in [0..30]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Table[n^5*(n^6 + 1)/2, {n, 0, 25}] (* G. C. Greubel, Jul 22 2016 *)
CoefficientList[Series[x  (1 + 1028 x + 76281 x^2 + 1101744 x^3 + 4869222 x^4 + 7861848 x^5 + 4869222 x^6 + 1101744 x^7 + 76281 x^8 + 1028 x^9 + x^10)/(1 - x)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Jul 23 2016 *)

Formula

G.f.: x*(1 + 1028*x + 76281*x^2 + 1101744*x^3 + 4869222*x^4 + 7861848*x^5 + 4869222*x^6 + 1101744*x^7 + 76281*x^8 + 1028*x^9 + x^10)/(1-x)^12. - Vincenzo Librandi, Jul 23 2016

a(n) = 12*a(n-1)-66*a(n-2)+220*a(n-3)-495*a(n-4)+792*a(n-5)-924*a(n-6)+792*a(n-7)-495*a(n-8)+220*a(n-9)-66*a(n-10)+12*a(n-11)-a(n-12). - Wesley Ivan Hurt, Oct 02 2021