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

%S 1,25,600,14400,345600,8294400,199065600,4777574400,114661785600,

%T 2751882854400,66045188505600,1585084524134400,38042028579225600,

%U 913008685901414400,21912208461633945600,525893003079214694400,12621432073901152665600,302914369773627663974400

%N Expansion of g.f.: (1+x)/(1-24*x).

%H Kenny Lau, <a href="/A170744/b170744.txt">Table of n, a(n) for n = 0..724</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (24).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*25^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 25*24^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (25*exp(24*x) - 1)/24. - _G. C. Greubel_, Sep 25 2019

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

%t Join[{1},NestList[24#&,25,30]] (* _Harvey P. Dale_, Jan 19 2019 *)

%o (Python) for i in range(31):print(i,25*24**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

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

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

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

%o (GAP) k:=25;; 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