A014937 a(1)=1, a(n) = n*20^(n-1) + a(n-1).

1, 41, 1241, 33241, 833241, 20033241, 468033241, 10708033241, 241108033241, 5361108033241, 118001108033241, 2575601108033241, 55823601108033241, 1202703601108033241, 25778703601108033241, 550066703601108033241, 11691186703601108033241, 247620786703601108033241

Offset: 1

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..750
• Index entries for linear recurrences with constant coefficients, signature (41,-440,400).

Programs

Mathematica

RecurrenceTable[{a[1]==1,a[n]==n*20^(n-1)+a[n-1]},a,{n,20}] (* or *) LinearRecurrence[{41,-440,400},{1,41,1241},20] (* Harvey P. Dale, Jun 04 2012 *)

Formula

a(n) = 41*a(n-1) - 440*a(n-2) + 400*a(n-3), a(1)=1, a(2)=41, a(3)=1241. - Harvey P. Dale, Jun 04 2012

G.f.: -x/((x-1)*(-1+20*x)^2). - R. J. Mathar, Nov 07 2015

From Elmo R. Oliveira, May 16 2025: (Start)

E.g.f.: exp(x)*(1 + exp(19*x)*(380*x - 1))/361.

a(n) = (20^n*(19*n - 1) + 1)/361.

a(n) = 40*a(n-1) - 400*a(n-2) + 1 for n > 2. (End)