%I #35 Sep 08 2022 08:45:49

%S 1,18,306,5202,88434,1503378,25557426,434476242,7386096114,

%T 125563633938,2134581776946,36287890208082,616894133537394,

%U 10487200270135698,178282404592306866,3030800878069216722,51523614927176684274,875901453762003632658,14890324713954061755186

%N Expansion of g.f.: (1+x)/(1-17*x).

%H Kenny Lau, <a href="/A170737/b170737.txt">Table of n, a(n) for n = 0..812</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (17).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*18^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 18*17^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (18*exp(17*x) -1)/17. - _G. C. Greubel_, Sep 24 2019

%p k:=18; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019

%t Join[{1},18*17^Range[0,25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%t CoefficientList[Series[(1+x)/(1-17x),{x,0,30}],x] (* or *) LinearRecurrence[ {17},{1,18},30] (* or *) Join[{1},NestList[ 17#&,18,30]] (* _Harvey P. Dale_, Jul 11 2015 *)

%o (PARI) a(n)=18*17^n\17 \\ _Charles R Greathouse IV_, Jul 11 2016

%o (Python) for i in range(31):print(i,18*17**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 01 2017

%o (Magma) k:=18; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019

%o (Sage) k=18; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019

%o (GAP) k:=18;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019

%Y Cf. A003945, A097805.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 04 2009