%I #22 Sep 08 2022 08:45:49

%S 1,40,1560,60840,2372760,92537640,3608967960,140749750440,

%T 5489240267160,214080370419240,8349134446350360,325616243407664040,

%U 12699033492898897560,495262306223057004840,19315229942699223188760,753293967765269704361640

%N Expansion of g.f.: (1+x)/(1-39*x).

%H Vincenzo Librandi, <a href="/A170759/b170759.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 (39).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*40^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 40*39^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F a(0)=1, a(1)=40, a(n) = 39*a(n-1). - _Vincenzo Librandi_, Dec 10 2012

%F E.g.f.: (40*exp(39*x) - 1)/39. - _G. C. Greubel_, Oct 10 2019

%p k:=40; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019

%t CoefficientList[Series[(1+x)/(1-39*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)

%t With[{k = 40}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)

%o (Magma) [1] cat [40*39^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 11 2012

%o (PARI) vector(26, n, k=40; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019

%o (Sage) k=40; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019

%o (GAP) k:=40;; 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