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%I #21 Sep 08 2022 08:45:49
%S 1,39,1482,56316,2140008,81320304,3090171552,117426518976,
%T 4462207721088,169563893401344,6443427949251072,244850262071540736,
%U 9304309958718547968,353563778431304822784,13435423580389583265792,510546096054804164100096
%N Expansion of g.f.: (1+x)/(1-38*x).
%H Vincenzo Librandi, <a href="/A170758/b170758.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (38).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*39^k. - _Philippe Deléham_, Dec 04 2009
%F a(0)=1; for n>0, a(n) = 39*38^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F E.g.f.: (39*exp(38*x) - 1)/38. - _G. C. Greubel_, Oct 09 2019
%p k:=39; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019
%t CoefficientList[Series[(1+x)/(1-38x), {x, 0, 20}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%t With[{k = 39}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)
%o (Magma) [1] cat [39*38^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Apr 28 2014
%o (PARI) vector(26, n, k=39; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019
%o (Sage) k=39; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019
%o (GAP) k:=39;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 09 2019
%Y Cf. A003945.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 04 2009
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