A228293 a(n) = Sum_{k=1..9} n^k.

0, 9, 1022, 29523, 349524, 2441405, 12093234, 47079207, 153391688, 435848049, 1111111110, 2593742459, 5628851292, 11488207653, 22250358074, 41189313615, 73300775184, 125999618777, 210027483918, 340614792099, 538947368420, 833994048909, 1264758228162

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).

Formula

G.f.: x*(x^8 +332*x^7 +11388*x^6 +77356*x^5 +153950*x^4 +99204*x^3 +19708*x^2 +932*x+9) / (x-1)^10.

a(1) = 9, else a(n) = (n^10-n)/(n-1).

a(0)=0, a(1)=9, a(2)=1022, a(3)=29523, a(4)=349524, a(5)=2441405, a(6)=12093234, a(7)=47079207, a(8)=153391688, a(9)=435848049, a(n) = 10*a(n-1) -45*a(n-2) +120*a(n-3) -210*a(n-4) +252*a(n-5) -210*a(n-6) +120*a(n-7) -45*a(n-8) +10*a(n-9) -a(n-10). - Harvey P. Dale, Dec 12 2013

a(n) = n*A102909(n). - Bruce Nye, Jan 16 2026

Maple

a:= n-> `if`(n=1, 9, (n^10-n)/(n-1)):
seq(a(n), n=0..30);

Mathematica

Table[Total[n^Range[9]], {n, 0, 30}] (* Harvey P. Dale, Dec 12 2013 *)
(* Alternative: *)
LinearRecurrence[ {10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 9, 1022, 29523, 349524, 2441405, 12093234, 47079207, 153391688, 435848049}, 30] (* Harvey P. Dale, Dec 12 2013 *)

Crossrefs

Column k=9 of A228275.

Cf. A102909.

Sequence in context: A100601 A260029 A266321 * A197781 A197612 A004809

Adjacent sequences: A228290 A228291 A228292 * A228294 A228295 A228296

Keyword

nonn,easy,changed

Author

Alois P. Heinz, Aug 19 2013

Status

approved