A270567 Expansion of g.f. (1+4*x)/(1-5*x).

1, 9, 45, 225, 1125, 5625, 28125, 140625, 703125, 3515625, 17578125, 87890625, 439453125, 2197265625, 10986328125, 54931640625, 274658203125, 1373291015625, 6866455078125, 34332275390625, 171661376953125, 858306884765625, 4291534423828125, 21457672119140625, 107288360595703125

Offset: 0

Author

Colin Barker, Mar 19 2016

Keywords

• nonn
• easy

Comments

Partial sums are 1, 10, 55, 280, 1405, 7030, ...

Apparently a duplicate of A189274. - R. J. Mathar, May 13 2016

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5).

Crossrefs

Cf. A000351 (powers of 5), A128625 (1+3*x)/(1-5*x), A189274.

Programs

Mathematica

CoefficientList[Series[(1 + 4 x)/(1 - 5 x), {x, 0, 23}], x] (* Michael De Vlieger, Mar 19 2016 *)

PARI

Vec((1+4*x)/(1-5*x) + O(x^30))

Formula

G.f.: (1+4*x)/(1-5*x).

a(n) = 5*a(n-1) for n>1.

a(n) = 9*5^(n-1) for n>0.

E.g.f.: (9*exp(5*x) - 4)/5. - Elmo R. Oliveira, Mar 25 2025