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%I #34 Sep 08 2022 08:45:49
%S 1,19,342,6156,110808,1994544,35901792,646232256,11632180608,
%T 209379250944,3768826516992,67838877305856,1221099791505408,
%U 21979796247097344,395636332447752192,7121453984059539456,128186171713071710208,2307351090835290783744,41532319635035234107392
%N Expansion of g.f.: (1+x)/(1-18*x).
%H Kenny Lau, <a href="/A170738/b170738.txt">Table of n, a(n) for n = 0..796</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (18).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*19^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 19*18^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (19*exp(18*x) -1)/18. - _G. C. Greubel_, Sep 24 2019
%p k:=19; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019
%t Join[{1},19*18^Range[0,25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%t CoefficientList[Series[(1+x)/(1-18x),{x,0,20}],x] (* or *) LinearRecurrence[ {18},{1,19},20] (* _Harvey P. Dale_, Jul 01 2017 *)
%o (Python) for i in range(31):print(i,19*18**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 01 2017
%o (PARI) vector(26, n, k=19; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019
%o (Magma) k:=19; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019
%o (Sage) k=19; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) k:=19;; 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
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