A270472 Expansion of g.f. (1-2*x)/(1-9*x).

1, 7, 63, 567, 5103, 45927, 413343, 3720087, 33480783, 301327047, 2711943423, 24407490807, 219667417263, 1977006755367, 17793060798303, 160137547184727, 1441237924662543, 12971141321962887, 116740271897665983, 1050662447078993847, 9455962023710944623, 85103658213398501607

Offset: 0

Author

Colin Barker, Mar 17 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9).

Crossrefs

Cf. A001019 (powers of 9), A005032, A187709 (partial sums).

Cf. A055275: (1-x)/(1-9*x); A092810: (1-3*x)/(1-9*x).

Programs

Mathematica

CoefficientList[Series[(1 - 2 x)/(1 - 9 x), {x, 0, 20}], x] (* Michael De Vlieger, Mar 18 2016 *)

PARI

Vec((1-2*x)/(1-9*x) + O(x^30))

Formula

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

a(n) = 9*a(n-1) for n>1.

a(n) = 7*9^(n-1) for n>0.

a(n) = A005032(2*n-2). - R. J. Mathar, Jan 28 2025

E.g.f.: (7*exp(9*x) + 2)/9. - Elmo R. Oliveira, Mar 25 2025