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

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (20, -100).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A081109, A081108.

Sequence in context: A060498 A274119 A171316 * A004190 A089707 A223391

Adjacent sequences: A081119 A081120 A081121 * A081123 A081124 A081125

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved