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Expansion of g.f.: (1+x)/(1-25*x).
50

%I #24 Sep 08 2022 08:45:49

%S 1,26,650,16250,406250,10156250,253906250,6347656250,158691406250,

%T 3967285156250,99182128906250,2479553222656250,61988830566406250,

%U 1549720764160156250,38743019104003906250,968575477600097656250,24214386940002441406250,605359673500061035156250

%N Expansion of g.f.: (1+x)/(1-25*x).

%H Kenny Lau, <a href="/A170745/b170745.txt">Table of n, a(n) for n = 0..715</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (25).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*26^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 26*25^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (26*exp(25*x) - 1)/25. - _G. C. Greubel_, Sep 25 2019

%p k:=26; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 25 2019

%t CoefficientList[Series[(1+x)/(1-25*x),{x,0,20}],x] (* or *) Join[ {1}, NestList[25#&,26,20]] (* _Harvey P. Dale_, Aug 08 2019 *)

%o (Python) for i in range(31):print(i,26*25**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

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

%o (Magma) k:=26; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 25 2019

%o (Sage) k=26; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019

%o (GAP) k:=26;; 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