A016261 Expansion of 1/((1-x)*(1-9*x)*(1-10*x)).

1, 20, 291, 3730, 44681, 513240, 5730271, 62683550, 675263061, 7188478660, 75807419051, 793377882570, 8251512054241, 85374719599280, 879483587504631, 9026463398652790, 92349281698986221, 942254646401987100, 9591402928728995011, 97433737469672066210

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-109,90).

Crossrefs

Cf. A016218, A016228.

Programs

Mathematica

Table[(2^(n + 4)*5^(n + 1) - 9^(n + 2) + 1)/72, {n, 40}] (* or *) CoefficientList[Series[1/((1 - z) (1 - 9*z) (1 - 10*z)), {z, 0, 40}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 21 2011 *)

Formula

a(n) = (8*10^(n+2) - 9^(n+3) + 1)/72. - Bruno Berselli, Mar 21 2011

a(n) = 19*a(n-1) - 90*a(n-2) + 1, n >= 2. - Vincenzo Librandi, Mar 21 2011