%I #20 Sep 08 2022 08:45:49

%S 1,47,2162,99452,4574792,210440432,9680259872,445291954112,

%T 20483429889152,942237774900992,43342937645445632,1993775131690499072,

%U 91713656057762957312,4218828178657096036352,194066096218226417672192,8927040426038415212920832

%N Expansion of g.f.: (1+x)/(1-46*x).

%H Vincenzo Librandi, <a href="/A170766/b170766.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 (46).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*47^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 47*46^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (47*exp(46*x) - 1)/46. - _G. C. Greubel_, Oct 11 2019

%p k:=47; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019

%t CoefficientList[Series[(1+x)/(1-46*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2012 *)

%t With[{k = 47}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)

%o (PARI) vector(26, n, k=47; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019

%o (Magma) k:=47; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019

%o (Sage) k=47; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019

%o (GAP) k:=47;; 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