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A170753 Expansion of g.f.: (1+x)/(1-33*x).

%I A170753 #28 Oct 10 2024 05:09:48
%S A170753 1,34,1122,37026,1221858,40321314,1330603362,43909910946,
%T A170753 1449027061218,47817893020194,1577990469666402,52073685498991266,
%U A170753 1718431621466711778,56708243508401488674,1871372035777249126242,61755277180649221165986,2037924146961424298477538
%N A170753 Expansion of g.f.: (1+x)/(1-33*x).
%H A170753 Kenny Lau, <a href="/A170753/b170753.txt">Table of n, a(n) for n = 0..658</a>
%H A170753 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (33).
%F A170753 a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*34^k. - _Philippe Deléham_, Dec 04 2009
%F A170753 a(0) = 1; for n>0, a(n) = 34*33^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F A170753 E.g.f.: (1/33)*(34*exp(33*x) - 1). - _Stefano Spezia_, Oct 09 2019
%p A170753 k:=34; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Oct 09 2019
%t A170753 With[{k = 34}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Oct 09 2019 *)
%o A170753 (Python) for i in range(1001):print(i,34*33**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017
%o A170753 (PARI) vector(26, n, k=34; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Oct 09 2019
%o A170753 (Magma) k:=34; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Oct 09 2019
%o A170753 (Sage) k=34; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Oct 09 2019
%o A170753 (GAP) k:=34;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Oct 09 2019
%Y A170753 Cf. A003945.
%K A170753 nonn,easy
%O A170753 0,2
%A A170753 _N. J. A. Sloane_, Dec 04 2009