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%I #18 Sep 08 2022 08:45:49
%S 1,49,2352,112896,5419008,260112384,12485394432,599298932736,
%T 28766348771328,1380784741023744,66277667569139712,
%U 3181328043318706176,152703746079297896448,7329779811806299029504,351829430966702353416192,16887812686401712963977216
%N Expansion of g.f.: (1+x)/(1-48*x).
%H Vincenzo Librandi, <a href="/A170768/b170768.txt">Table of n, a(n) for n = 0..600</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (48).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*49^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 49*48^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (49*exp(48*x) - 1)/48. - _G. C. Greubel_, Oct 11 2019
%p k:=49; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019
%t CoefficientList[Series[(1+x)/(1-48*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2012 *)
%t With[{k = 49}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)
%o (PARI) vector(26, n, k=49; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019
%o (Magma) k:=49; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019
%o (Sage) k=49; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019
%o (GAP) k:=49;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 10 2019
%Y Cf. A003945.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 04 2009
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