A126431 a(n) = n*10^n.

0, 10, 200, 3000, 40000, 500000, 6000000, 70000000, 800000000, 9000000000, 100000000000, 1100000000000, 12000000000000, 130000000000000, 1400000000000000, 15000000000000000, 160000000000000000, 1700000000000000000, 18000000000000000000, 190000000000000000000

Offset: 0

Author

Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 11 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (20,-100).

Crossrefs

Cf. A011557.

Programs

Magma

[n*10^n: n in [0..20]]; // Vincenzo Librandi, Sep 09 2014

Maple

A126431 := proc(n) n*10^n ; end proc: # Bruno Berselli, Sep 09 2014

Mathematica

Table[n 10^n,{n,0,20}] (* or *) LinearRecurrence[{20,-100},{0,10},20] (* Harvey P. Dale, Mar 30 2012 *)
CoefficientList[Series[10 x/(1 - 10 x)^2, {x, 0, 20}], x] (* Vincenzo Librandi, Sep 09 2014 *)

PARI

a(n)=n*10^n \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(0)=0, a(1)=10; for n > 1, a(n) = 20*a(n-1) - 100*a(n-2). - Harvey P. Dale, Mar 30 2012

G.f.: 10*x/(1 - 10*x)^2. - Vincenzo Librandi, Sep 09 2014

From Amiram Eldar, Jul 20 2020: (Start)

Sum_{n>=1} 1/a(n) = log(10/9).

Sum_{n>=1} (-1)^(n+1)/a(n) = log(11/10). (End)

From Elmo R. Oliveira, Sep 07 2024: (Start)

E.g.f.: 10*x*exp(10*x).

a(n) = n*A011557(n). (End)