login
Expansion of g.f.: (1+x)/(1-34*x).
50

%I #21 Sep 08 2022 08:45:49

%S 1,35,1190,40460,1375640,46771760,1590239840,54068154560,

%T 1838317255040,62502786671360,2125094746826240,72253221392092160,

%U 2456609527331133440,83524723929258536960,2839840613594790256640,96554580862222868725760,3282855749315577536675840

%N Expansion of g.f.: (1+x)/(1-34*x).

%H G. C. Greubel, <a href="/A170754/b170754.txt">Table of n, a(n) for n = 0..649</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (34).

%F a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*35^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 35*34^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (1/34)*(35*exp(34*x) - 1). - _Stefano Spezia_, Oct 09 2019

%p k:=35; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019

%t CoefficientList[Series[(1+x)/(1-34x),{x,0,30}],x] (* _Harvey P. Dale_, Aug 23 2016 *)

%t With[{k = 35}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)

%o (PARI) vector(26, n, k=35; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019

%o (Magma) k:=35; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019

%o (Sage) k=35; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019

%o (GAP) k:=35;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 09 2019

%Y Cf. A003945.

%K nonn,easy

%O 0,2

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