A170739 Expansion of g.f.: (1+x)/(1-19*x).

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420, 303622540597495965980, 5768828271352423353620, 109607737155696043718780

Offset: 0

Author

N. J. A. Sloane, Dec 04 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (19).

Crossrefs

Cf. A003945, A097805.

Programs

GAP

k:=20;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Magma

[1] cat [20*19^(n-1): n in [1..20]]; // Vincenzo Librandi, Dec 05 2012

Maple

k:=20; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # G. C. Greubel, Sep 24 2019

Mathematica

Join[{1}, 20*19^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *)
CoefficientList[Series[(1+x)/(1-19x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 05 2012 *)
Join[{1},NestList[19#&,20,20]] (* Harvey P. Dale, Nov 26 2022 *)

PARI

a(n)=20*19^n\19 \\ Charles R Greathouse IV, Jul 01 2013

Sage

k=20; [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)*20^k. - Philippe Deléham, Dec 04 2009

a(0) = 1; for n>0, a(n) = 20*19^(n-1). - Vincenzo Librandi, Dec 05 2009

a(0) = 1, a(1) = 20; for n>1, a(n) = 19*a(n-1). - Vincenzo Librandi, Dec 05 2012

E.g.f.: (20*exp(19*x) - 1)/19. - G. C. Greubel, Sep 24 2019