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%I #15 Aug 01 2015 10:45:06
%S 0,9,1022,29523,349524,2441405,12093234,47079207,153391688,435848049,
%T 1111111110,2593742459,5628851292,11488207653,22250358074,41189313615,
%U 73300775184,125999618777,210027483918,340614792099,538947368420,833994048909,1264758228162
%N a(n) = Sum_{k=1..9} n^k.
%H Alois P. Heinz, <a href="/A228293/b228293.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10, -45, 120, -210, 252, -210, 120, -45, 10, -1).
%F 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.
%F a(1) = 9, else a(n) = (n^10-n)/(n-1).
%F 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
%p a:= n-> `if`(n=1, 9, (n^10-n)/(n-1)):
%p seq(a(n), n=0..30);
%t Table[Total[n^Range[9]],{n,0,30}] (* or *) 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 *)
%Y Column k=9 of A228275.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Aug 19 2013
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