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%I #21 Sep 08 2022 08:45:49
%S 1,50,2450,120050,5882450,288240050,14123762450,692064360050,
%T 33911153642450,1661646528480050,81420679895522450,
%U 3989613314880600050,195491052429149402450,9579061569028320720050,469374016882387715282450,22999326827236998048840050
%N Expansion of g.f.: (1+x)/(1-49*x).
%H Vincenzo Librandi, <a href="/A170769/b170769.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 (49).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*50^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 50*49^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (50*exp(49*x) - 1)/49. - _G. C. Greubel_, Oct 11 2019
%p k:=50; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019
%t CoefficientList[Series[(1+x)/(1-49*x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 09 2012 *)
%t With[{k = 50}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)
%o (Maxima) A170769(n):=if n=0 then 1 else 50*49^(n-1)$
%o makelist(A170769(n),n,0,30); /* _Martin Ettl_, Nov 06 2012 */
%o (PARI) vector(26, n, k=50; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 10 2019
%o (Magma) k:=50; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019
%o (Sage) k=50; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019
%o (GAP) k:=50;; 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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