Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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