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A081044
9th binomial transform of (1,8,0,0,0,0,0,0,.....).
3
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
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
Sequence in context: A016281 A160398 A181380 * A016227 A155001 A012095
KEYWORD
base,easy,nonn
AUTHOR
Paul Barry, Mar 04 2003
STATUS
approved