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%I #25 Jun 19 2023 11:49:22
%S 1,41,1640,65600,2624000,104960000,4198400000,167936000000,
%T 6717440000000,268697600000000,10747904000000000,429916160000000000,
%U 17196646400000000000,687865856000000000000,27514634240000000000000,1100585369600000000000000
%N Expansion of g.f.: (1+x)/(1-40*x).
%H Vincenzo Librandi, <a href="/A170760/b170760.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 (40).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*41^k. - _Philippe Deléham_, Dec 04 2009
%F a(0)=1; for n>0, a(n) = 41*40^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F a(0)=1, a(1)=41, a(n) = 40*a(n-1). - _Vincenzo Librandi_, Dec 10 2012
%F E.g.f.: (41*exp(40*x) - 1)/40. - _G. C. Greubel_, Oct 10 2019
%p k:=41; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019
%t CoefficientList[Series[(1+x)/(1-40*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)
%t With[{k = 41}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)
%t Join[{1},NestList[40#&,41,20]] (* _Harvey P. Dale_, Jun 19 2023 *)
%o (PARI) vector(26, n, k=41; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019
%o (Magma) k:=41; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019
%o (Sage) k=41; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019
%o (GAP) k:=41;; 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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