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a(n) = n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
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%I #27 Mar 12 2024 08:47:53

%S 1,10,1023,29524,349525,2441406,12093235,47079208,153391689,435848050,

%T 1111111111,2593742460,5628851293,11488207654,22250358075,41189313616,

%U 73300775185,125999618778,210027483919,340614792100,538947368421,833994048910,1264758228163

%N a(n) = n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.

%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.: (341*x^8 +11352*x^7 +77440*x^6 +153824*x^5 +99330*x^4 +19624*x^3 +968*x^2 +1)/(x -1)^10. - _Colin Barker_, Oct 29 2012

%F a(n) = (n^10-1)/(n-1) with a(1) = 10. - _Arkadiusz Wesolowski_, Mar 30 2013

%t With[{eq=Total[n^Range[0,9]]},Table[eq,{n,0,20}]] (* _Harvey P. Dale_, Dec 16 2011 *)

%o (PARI) a(n)=n^9+n^8+n^7+n^6+n^5+n^4+n^3+n^2+n+1 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A001017.

%K nonn,easy

%O 0,2

%A Douglas Winston (douglas.winston(AT)srupc.com), Mar 25 2005