A170737 Expansion of g.f.: (1+x)/(1-17*x).

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274, 875901453762003632658, 14890324713954061755186

Offset

0,2

Links

Kenny Lau, Table of n, a(n) for n = 0..812

Index entries for linear recurrences with constant coefficients, signature (17).

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*18^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 18*17^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (18*exp(17*x) -1)/17. - G. C. Greubel, Sep 24 2019

Maple

k:=18; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 18*17^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-17x), {x, 0, 30}], x] (* or *) LinearRecurrence[ {17}, {1, 18}, 30] (* or *) Join[{1}, NestList[ 17#&, 18, 30]] (* Harvey P. Dale, Jul 11 2015 *)

Prog

(PARI) a(n)=18*17^n\17 \\ Charles R Greathouse IV, Jul 11 2016
(Python) for i in range(31):print(i, 18*17**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017
(Magma) k:=18; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
(Sage) k=18; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
(GAP) k:=18;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A003945, A097805.

Sequence in context: A170603 A170651 A170699 * A091045 A179121 A226298

Adjacent sequences: A170734 A170735 A170736 * A170738 A170739 A170740

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved