A081044 9th binomial transform of (1,8,0,0,0,0,0,0,.....).

1, 17, 225, 2673, 29889, 321489, 3365793, 34543665, 349156737, 3486784401, 34480423521, 338218086897, 3295011258945, 31914537622353, 307565765227809, 2951106226689969, 28207085096966913, 268687927383516945

Offset: 0

Author

Paul Barry, Mar 04 2003

Keywords

• base
• easy
• nonn

Comments

Also number of (n+1)-digit numbers with exactly one '9' in their decimal expansion. Nine can be replaced by any nonzero digit 1..9. - Zak Seidov, Jul 11 2016

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (18,-81).

Crossrefs

Cf. A081043, A081045.

Programs

Mathematica

Table[(8n+9)9^(n-1),{n,0,30}] (*or*) LinearRecurrence[{18, -81}, {1, 17}, 40] (* Vincenzo Librandi, Feb 23 2012 *)

PARI

a(n) = (8*n+9)*9^(n-1); \\ Altug Alkan, Jul 18 2016

Formula

a(n) = 18*a(n-1)-81*a(n-2), a(0)=0, a(1)=17.

a(n) = (8n+9)*9^(n-1).

a(n) = Sum_{k=0..n} (k+1)*8^k*binomial(n, k).

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

E.g.f.: (1 + 8*x)*exp(9*x). - Ilya Gutkovskiy, Jul 18 2016