A081122 10th binomial transform of (1,1,0,0,0,0,...).

1, 11, 120, 1300, 14000, 150000, 1600000, 17000000, 180000000, 1900000000, 20000000000, 210000000000, 2200000000000, 23000000000000, 240000000000000, 2500000000000000, 26000000000000000, 270000000000000000

Offset: 0

Author

Paul Barry, Mar 07 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (20, -100).

Crossrefs

Cf. A081109, A081108.

Programs

Magma

[(n+10)*10^(n-1): n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Mathematica

CoefficientList[Series[(1 - 9 x) / (1 - 10 x)^2, {x, 0, 20}], x] (* Vincenzo Librandi, Aug 06 2013 *)

Formula

a(n) = 20*a(n-1) - 100*a(n-2), a(0) = 1, a(1) = 11.

a(n) = (n + 10)*10^(n-1).

G.f.: (1 - 9*x)/(1 - 10*x)^2.

E.g.f.: exp(10*x)*(1 + x). - Stefano Spezia, Mar 04 2023