A177069 11^n + n^11.

1, 12, 2169, 178478, 4208945, 48989176, 364568617, 1996813914, 8804293473, 33739007300, 125937424601, 570623341222, 3881436747409, 36314872537968, 383799398752905, 4185897925275026, 45967322049616577, 505481300395601404

Offset: 0

Author

Vincenzo Librandi, May 31 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..950
• Index entries for linear recurrences with constant coefficients, signature (23,-198,946,-2915,6237,-9636,10956,-9207,5665,-2486,738,-133,11).

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), A185277 (k=9), A177068 (k=10), this sequence (k=11).

Programs

Magma

[11^n+n^11: n in [0..20]]

Mathematica

Table[11^n + n^11, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 11 x + 2091 x^2 + 130021 x^3 + 524976 x^4 -14501046 x^5 - 91394082 x^6 - 163229406 x^7 - 104915271 x^8 - 24085951 x^9 - 1676905 x^10 - 22407 x^11 - 10 x^12)/((1 - x)^12 (1 - 11 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 28 2014 *)

PARI

a(n)= 11^n+n^11 \\ Charles R Greathouse IV, Jan 11 2012

Sage

[11^n+n^11 for n in (0..30)] # Bruno Berselli, Aug 28 2014

Formula

G.f.: (1 - 11*x + 2091*x^2 + 130021*x^3 + 524976*x^4 - 14501046*x^5 - 91394082*x^6 - 163229406*x^7 - 104915271*x^8 - 24085951*x^9 - 1676905*x^10 - 22407*x^11 - 10*x^12) / ((1-x)^12*(1-11*x)). - Vincenzo Librandi, Aug 28 2014