A185277 a(n) = n^9 + 9^n.

1, 10, 593, 20412, 268705, 2012174, 10609137, 45136576, 177264449, 774840978, 4486784401, 33739007300, 287589316833, 2552470327702, 22897453501745, 205929575454024, 1853088908328577, 16677300287543066, 150094833656289489

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Feb 19 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (19,-135,525,-1290,2142,-2478,2010,-1125,415,-91,9).

Crossrefs

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).

Programs

Magma

[9^n+n^9: n in [0..30]]; // Vincenzo Librandi, Oct 27 2011

Mathematica

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 *)
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 *)

PARI

for(n=0,25, print1(n^9 + 9^n, ", ")) \\ G. C. Greubel, Jun 25 2017

Sage

[9^n+n^9 for n in (0..30)] # Bruno Berselli, Aug 28 2014

Formula

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