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A170765 Expansion of g.f.: (1+x)/(1-45*x). 50

%I

%S 1,46,2070,93150,4191750,188628750,8488293750,381973218750,

%T 17188794843750,773495767968750,34807309558593750,1566328930136718750,

%U 70484801856152343750,3171816083526855468750,142731723758708496093750,6422927569141882324218750

%N Expansion of g.f.: (1+x)/(1-45*x).

%H Vincenzo Librandi, <a href="/A170765/b170765.txt">Table of n, a(n) for n = 0..600</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (45).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*46^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 46*45^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (46*exp(45*x) - 1)/45. - _G. C. Greubel_, Oct 10 2019

%p k:=46; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019

%t CoefficientList[Series[(1+x)/(1-45x),{x,0,15}],x] (* _Harvey P. Dale_, Mar 26 2011 *)

%t With[{k = 46}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)

%o (PARI) a(n)=46*45^n\45 \\ _Charles R Greathouse IV_, Jun 16 2011

%o (PARI) vector(26, n, k=46; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019

%o (MAGMA) k:=46; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019

%o (Sage) k=46; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019

%o (GAP) k:=46;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 10 2019

%Y Cf. A003945.

%K nonn,easy

%O 0,2

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

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Last modified September 18 04:14 EDT 2020. Contains 337165 sequences. (Running on oeis4.)