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

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Kenny Lau, Table of n, a(n) for n = 0..812
• Index entries for linear recurrences with constant coefficients, signature (17).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=18;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

k:=18; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // 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 *)

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

Sage

k=18; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019

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