A170738 Expansion of g.f.: (1+x)/(1-18*x).

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539456, 128186171713071710208, 2307351090835290783744, 41532319635035234107392

Offset

0,2

Links

Kenny Lau, Table of n, a(n) for n = 0..796

Index entries for linear recurrences with constant coefficients, signature (18).

Formula

a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*19^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 19*18^(n-1). - Vincenzo Librandi, Dec 05 2009

E.g.f.: (19*exp(18*x) -1)/18. - G. C. Greubel, Sep 24 2019

Maple

k:=19; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 19*18^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-18x), {x, 0, 20}], x] (* or *) LinearRecurrence[ {18}, {1, 19}, 20] (* Harvey P. Dale, Jul 01 2017 *)

Prog

(Python) for i in range(31):print(i, 19*18**(i-1) if i>0 else 1) # Kenny Lau, Aug 01 2017
(PARI) vector(26, n, k=19; if(n==1, 1, k*(k-1)^(n-2))) \\ G. C. Greubel, Sep 24 2019
(Magma) k:=19; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
(Sage) k=19; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
(GAP) k:=19;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A003945, A097805.

Sequence in context: A170604 A170652 A170700 * A218721 A282030 A192568

Adjacent sequences: A170735 A170736 A170737 * A170739 A170740 A170741

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 04 2009

Status

approved