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Expansion of g.f.: (1+x)/(1-47*x).
50

%I #25 Sep 08 2022 08:45:49

%S 1,48,2256,106032,4983504,234224688,11008560336,517402335792,

%T 24317909782224,1142941759764528,53718262708932816,

%U 2524758347319842352,118663642324032590544,5577191189229531755568,262127985893787992511696,12320015337008035648049712

%N Expansion of g.f.: (1+x)/(1-47*x).

%H Vincenzo Librandi, <a href="/A170767/b170767.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 (47).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*48^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 48*47^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (48*exp(47*x) - 1)/47. - _G. C. Greubel_, Oct 11 2019

%p k:=48; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019

%t CoefficientList[Series[(1+x)/(1-47*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2012 *)

%t With[{k = 48}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)

%t Join[{1},NestList[47#&,48,20]] (* _Harvey P. Dale_, Nov 07 2021 *)

%o (PARI) vector(26, n, k=48; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019

%o (Magma) k:=48; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019

%o (Sage) k=48; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019

%o (GAP) k:=48;; 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