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

0,2

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).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A081043, A081045.

Sequence in context: A016281 A160398 A181380 * A016227 A155001 A012095

Adjacent sequences: A081041 A081042 A081043 * A081045 A081046 A081047

Keyword

base,easy,nonn

Author

Paul Barry, Mar 04 2003

Status

approved