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%I #24 Sep 08 2022 08:45:49
%S 1,27,702,18252,474552,12338352,320797152,8340725952,216858874752,
%T 5638330743552,146596599332352,3811511582641152,99099301148669952,
%U 2576581829865418752,66991127576500887552,1741769316989023076352,45286002241714599985152,1177436058284579599613952
%N Expansion of g.f.: (1+x)/(1-26*x).
%H Kenny Lau, <a href="/A170746/b170746.txt">Table of n, a(n) for n = 0..706</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (26).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*27^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 27*26^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (27*exp(26*x) - 1)/26. - _G. C. Greubel_, Sep 25 2019
%p k:=27; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 25 2019
%t CoefficientList[Series[(1+x)/(1-26x),{x,0,20}],x] (* or *) Join[ {1}, NestList[26#&,27,20]] (* _Harvey P. Dale_, Jun 16 2016 *)
%o (Python) for i in range(31):print(i,27*26**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017
%o (PARI) vector(26, n, k=27; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 25 2019
%o (Magma) k:=27; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 25 2019
%o (Sage) k=27; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 25 2019
%o (GAP) k:=27;; 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
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