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Expansion of g.f.: (1+x)/(1-35*x).
50

%I #19 Sep 08 2022 08:45:49

%S 1,36,1260,44100,1543500,54022500,1890787500,66177562500,

%T 2316214687500,81067514062500,2837362992187500,99307704726562500,

%U 3475769665429687500,121651938290039062500,4257817840151367187500,149023624405297851562500

%N Expansion of g.f.: (1+x)/(1-35*x).

%H G. C. Greubel, <a href="/A170755/b170755.txt">Table of n, a(n) for n = 0..644</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (35).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*36^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 36*35^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (1/35)*(36*exp(35*x) - 1). - _Stefano Spezia_, Oct 09 2019

%p k:=36; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019

%t With[{k = 36}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)

%o (PARI) vector(26, n, k=36; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019

%o (Magma) k:=36; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019

%o (Sage) k=36; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019

%o (GAP) k:=36;; 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