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%I #22 Jun 08 2023 13:50:17
%S 1,10,593,20412,268705,2012174,10609137,45136576,177264449,774840978,
%T 4486784401,33739007300,287589316833,2552470327702,22897453501745,
%U 205929575454024,1853088908328577,16677300287543066,150094833656289489
%N a(n) = n^9 + 9^n.
%H Vincenzo Librandi, <a href="/A185277/b185277.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (19,-135,525,-1290,2142,-2478,2010,-1125,415,-91,9).
%F G.f.: (1 - 9*x + 538*x^2 + 9970*x^3 - 43028*x^4 - 638168*x^5-1317266*x^6 - 779618*x^7 - 130925*x^8 - 4527*x^9 - 8*x^10)/((1-x)^10*(1-9*x)). - _Vincenzo Librandi_, Aug 28 2014
%t Table[9^n + n^9, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 9 x + 538 x^2 + 9970 x^3 - 43028 x^4 - 638168 x^5 - 1317266 x^6 - 779618 x^7 - 130925 x^8 - 4527 x^9 - 8 x^10)/((1 - x)^10 (1 - 9 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 28 2014 *)
%t LinearRecurrence[{19,-135,525,-1290,2142,-2478,2010,-1125,415,-91,9},{1,10,593,20412,268705,2012174,10609137,45136576,177264449,774840978,4486784401},20] (* _Harvey P. Dale_, Jun 08 2023 *)
%o (Magma) [9^n+n^9: n in [0..30]]; // _Vincenzo Librandi_, Oct 27 2011
%o (Sage) [9^n+n^9 for n in (0..30)] # _Bruno Berselli_, Aug 28 2014
%o (PARI) for(n=0,25, print1(n^9 + 9^n, ", ")) \\ _G. C. Greubel_, Jun 25 2017
%Y Cf. sequences of the form k^n+n^k: A001580 (k=2), A001585 (k=3), A001589 (k=4), A001593 (k=5), A001594 (k=6), A001596 (k=7), A198401 (k=8), this sequence (k=9), A177068 (k=10), A177069 (k=11).
%K nonn,easy
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011
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