login
Expansion of g.f.: (1+x)/(1-27*x).
50

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

%S 1,28,756,20412,551124,14880348,401769396,10847773692,292889889684,

%T 7908027021468,213516729579636,5764951698650172,155653695863554644,

%U 4202649788315975388,113471544284531335476,3063731695682346057852,82720755783423343562004,2233460406152430276174108

%N Expansion of g.f.: (1+x)/(1-27*x).

%H Kenny Lau, <a href="/A170747/b170747.txt">Table of n, a(n) for n = 0..698</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (27).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*28^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n > 0, a(n) = 28*27^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (28*exp(27*x) - 1)/27. - _G. C. Greubel_, Sep 25 2019

%p k:=28; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 25 2019

%t With[{k=28}, Table[If[n==0,1, k*(k-1)^(n-1)], {n,0,25}]] (* _G. C. Greubel_, Sep 25 2019 *)

%o (Python) for i in range(31):print(i,28*27**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

%o (PARI) vector(26, n, k=28; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 25 2019

%o (Magma) k:=28; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 25 2019

%o (Sage) k=28; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 25 2019

%o (GAP) k:=28;; 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