%I #29 Sep 25 2024 16:56:23

%S 1,31,930,27900,837000,25110000,753300000,22599000000,677970000000,

%T 20339100000000,610173000000000,18305190000000000,549155700000000000,

%U 16474671000000000000,494240130000000000000,14827203900000000000000,444816117000000000000000

%N Expansion of g.f.: (1+x)/(1-30*x).

%H Kenny Lau, <a href="/A170750/b170750.txt">Table of n, a(n) for n = 0..676</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (30).

%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*31^k. - _Philippe Deléham_, Dec 04 2009

%F a(0) = 1; for n>0, a(n) = 31*30^(n-1). - _Vincenzo Librandi_, Dec 05 2009

%F E.g.f.: (31*exp(30*x) - 1)/30. - _G. C. Greubel_, Sep 25 2019

%p k:=31; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 25 2019

%t CoefficientList[Series[(1+x)/(1-30x), {x, 0, 25}], x] (* _Michael De Vlieger_, Aug 04 2017 *)

%t With[{k = 31}, Table[If[n==0, 1, k*(k-1)^(n-1)], {n, 0, 25}]] (* _G. C. Greubel_, Sep 25 2019 *)

%t LinearRecurrence[{30},{1,31},20] (* _Harvey P. Dale_, Sep 25 2024 *)

%o (Python) for i in range(31):print(i,31*30**(i-1) if i>0 else 1) # _Kenny Lau_, Aug 03 2017

%o (PARI) vector(26, n, k=31; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 25 2019

%o (Magma) k:=31; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 25 2019

%o (Sage) k=31; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 25 2019

%o (GAP) k:=31;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 25 2019

%Y Cf. A003945, A097805.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 04 2009