A228292 a(n) = Sum_{k=1..8} n^k.

0, 8, 510, 9840, 87380, 488280, 2015538, 6725600, 19173960, 48427560, 111111110, 235794768, 469070940, 883708280, 1589311290, 2745954240, 4581298448, 7411742280, 11668193550, 17927094320, 26947368420, 39714002328, 57489010370, 81870575520, 114861197400

Offset: 0

Author

Alois P. Heinz, Aug 19 2013

Keywords

• nonn
• easy

Links

• Alois P. Heinz, 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

Column k=8 of A228275.

Programs

Maple

a:= n-> `if`(n=1, 8, (n^9-n)/(n-1)):
seq(a(n), n=0..30);

Mathematica

Table[Total[n^Range[8]],{n,0,30}] (* or *) LinearRecurrence[ {9,-36,84,-126,126,-84,36,-9,1},{0,8,510,9840,87380,488280,2015538,6725600,19173960},30] (* Harvey P. Dale, Jan 28 2014 *)

Formula

G.f.: -2*x*(85*x^6+1695*x^5+7134*x^4+8254*x^3+2769*x^2+219*x+4)/(x-1)^9.

a(1) = 8, else a(n) = (n^9-n)/(n-1).

a(0)=0, a(1)=8, a(2)=510, a(3)=9840, a(4)=87380, a(5)=488280, a(6)=2015538, a(7)=6725600, a(8)=19173960, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)- 84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Jan 28 2014