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A170739 Expansion of g.f.: (1+x)/(1-19*x). 50

%I

%S 1,20,380,7220,137180,2606420,49521980,940917620,17877434780,

%T 339671260820,6453753955580,122621325156020,2329805177964380,

%U 44266298381323220,841059669245141180,15980133715657682420,303622540597495965980,5768828271352423353620,109607737155696043718780

%N Expansion of g.f.: (1+x)/(1-19*x).

%H Vincenzo Librandi, <a href="/A170739/b170739.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (19).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*20^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 20*19^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F a(0) = 1, a(1) = 20; for n>1, a(n) = 19*a(n-1). - _Vincenzo Librandi_, Dec 05 2012

%F E.g.f.: (20*exp(19*x) - 1)/19. - _G. C. Greubel_, Sep 24 2019

%p k:=20; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019

%t Join[{1}, 20*19^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%t CoefficientList[Series[(1+x)/(1-19x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05.2012 *)

%o (MAGMA) [1] cat [20*19^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 05 2012

%o (PARI) a(n)=20*19^n\19 \\ _Charles R Greathouse IV_, Jul 01 2013

%o (Sage) k=20; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019

%o (GAP) k:=20;; 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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Last modified October 19 21:28 EDT 2019. Contains 328244 sequences. (Running on oeis4.)