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A170736 Expansion of g.f.: (1+x)/(1-16*x). 50

%I

%S 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,

%T 73014444032,1168231104512,18691697672192,299067162755072,

%U 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592,313594649253062377472,5017514388048998039552

%N Expansion of g.f.: (1+x)/(1-16*x).

%H Vincenzo Librandi, <a href="/A170736/b170736.txt">Table of n, a(n) for n = 0..800</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (16).

%F a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*17^k. - _Philippe Deléham_, Dec 04 2009

%F a(n) = 17*16^(n-1). - _Vincenzo Librandi_, Dec 11 2012

%F a(0)=1, a(1)=17, a(n) = 16*a(n-1). - _Vincenzo Librandi_, Dec 11 2012

%F E.g.f.: (17*exp(16*x) - 1)/16. - _G. C. Greubel_, Sep 24 2019

%p k:=17; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019

%t Join[{1},17*16^Range[0,25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)

%t CoefficientList[Series[(1+x)/(1-16*x), {x, 0, 25}], x] (* _Vincenzo Librandi_, Dec 11 2012 *)

%o (MAGMA) [1] cat [17*16^(n-1): n in [1..25]]; // _Vincenzo Librandi_, Dec 11 2012

%o (PARI) vector(26, n, k=17; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019

%o (Sage) k=17; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019

%o (GAP) k:=17;; 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 16 06:21 EDT 2019. Contains 328048 sequences. (Running on oeis4.)