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Expansion of g.f.: (1+x)/(1-42*x).
51

%I #29 Oct 12 2024 01:41:11

%S 1,43,1806,75852,3185784,133802928,5619722976,236028364992,

%T 9913191329664,416354035845888,17486869505527296,734448519232146432,

%U 30846837807750150144,1295567187925506306048,54413821892871264854016,2285380519500593123868672

%N Expansion of g.f.: (1+x)/(1-42*x).

%H Vincenzo Librandi, <a href="/A170762/b170762.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 (42).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*43^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 43*42^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F a(0)=1, a(1)=43, a(n)=42*a(n-1). - _Harvey P. Dale_, Mar 26 2012

%F E.g.f.: (43*exp(42*x) - 1)/42. - _G. C. Greubel_, Oct 10 2019

%p k:=43; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 10 2019

%t CoefficientList[Series[(1+x)/(1-42x),{x,0,30}],x] (* or *) Join[{1}, NestList[42#&,43,30]] (* _Harvey P. Dale_, Mar 26 2012 *)

%t With[{k = 43}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 10 2019 *)

%o (PARI) a(n)=if(n,43*42^(n-1),1) \\ _Charles R Greathouse IV_, Mar 22 2016

%o (Magma) k:=43; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 10 2019

%o (Sage) k=43; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 10 2019

%o (GAP) k:=43;; 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