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 #22 Sep 08 2022 08:45:49
%S 1,17,272,4352,69632,1114112,17825792,285212672,4563402752,
%T 73014444032,1168231104512,18691697672192,299067162755072,
%U 4785074604081152,76561193665298432,1224979098644774912,19599665578316398592,313594649253062377472,5017514388048998039552
%N Expansion of g.f.: (1+x)/(1-16*x).
%H Vincenzo Librandi, <a href="/A170736/b170736.txt">Table of n, a(n) for n = 0..800</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (16).
%F a(n)= Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*17^k. - _Philippe Deléham_, Dec 04 2009
%F a(n) = 17*16^(n-1). - _Vincenzo Librandi_, Dec 11 2012
%F a(0)=1, a(1)=17, a(n) = 16*a(n-1). - _Vincenzo Librandi_, Dec 11 2012
%F E.g.f.: (17*exp(16*x) - 1)/16. - _G. C. Greubel_, Sep 24 2019
%p k:=17; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019
%t Join[{1},17*16^Range[0,25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%t CoefficientList[Series[(1+x)/(1-16*x), {x, 0, 25}], x] (* _Vincenzo Librandi_, Dec 11 2012 *)
%o (Magma) [1] cat [17*16^(n-1): n in [1..25]]; // _Vincenzo Librandi_, Dec 11 2012
%o (PARI) vector(26, n, k=17; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019
%o (Sage) k=17; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) k:=17;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019
%Y Cf. A003945, A097805.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 04 2009