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%I #23 Sep 08 2022 08:45:49
%S 1,45,1980,87120,3833280,168664320,7421230080,326534123520,
%T 14367501434880,632170063134720,27815482777927680,1223881242228817920,
%U 53850774658067988480,2369434084954991493120,104255099738019625697280,4587224388472863530680320
%N Expansion of g.f.: (1+x)/(1-44*x).
%H Vincenzo Librandi, <a href="/A170764/b170764.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 (44).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*45^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 45*44^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (45*exp(44*x) - 1)/44. - _G. C. Greubel_, Oct 10 2019
%p k:=45; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019
%t CoefficientList[Series[(1+x)/(1-44*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2012 *)
%t With[{k = 45}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)
%t Join[{1},NestList[44#&,45,20]] (* _Harvey P. Dale_, Aug 22 2021 *)
%o (PARI) vector(26, n, k=45; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019
%o (Magma) k:=45; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019
%o (Sage) k=45; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019
%o (GAP) k:=45;; 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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