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Expansion of g.f.: (1+x)/(1-29*x).
51

%I #28 Sep 08 2022 08:45:49

%S 1,30,870,25230,731670,21218430,615334470,17844699630,517496289270,

%T 15007392388830,435214379276070,12621216999006030,366015292971174870,

%U 10614443496164071230,307818861388758065670,8926746980273983904430,258875662427945533228470

%N Expansion of g.f.: (1+x)/(1-29*x).

%H Kenny Lau, <a href="/A170749/b170749.txt">Table of n, a(n) for n = 0..683</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (29).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*30^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n > 0, a(n) = 30*29^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (30*exp(29*x) -1)/29. - _G. C. Greubel_, Sep 25 2019

%p k:=30; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 25 2019

%t With[{k=30}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* _G. C. Greubel_, Sep 25 2019 *)

%t Join[{1},NestList[29#&,30,20]] (* _Harvey P. Dale_, Aug 27 2020 *)

%o (Python) for i in range(31):print(i,30*29**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

%o (PARI) vector(26, n, k=30; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 25 2019

%o (Magma) k:=30; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 25 2019

%o (Sage) k=30; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 25 2019

%o (GAP) k:=30;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 25 2019

%Y Cf. A003945, A097805.

%K nonn,easy

%O 0,2

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