A005053 Expand (1-2*x)/(1-5*x).

1, 3, 15, 75, 375, 1875, 9375, 46875, 234375, 1171875, 5859375, 29296875, 146484375, 732421875, 3662109375, 18310546875, 91552734375, 457763671875, 2288818359375, 11444091796875, 57220458984375

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) is the number of generalized compositions of n when there are 3*2^(i-1) different types of i, (i=1,2,...). - Milan Janjic, Sep 24 2010

INVERTi transform of A180034: (1, 4, 22, 124, 700, ...). - Gary W. Adamson, Aug 10 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 883

Crossrefs

Cf. A180034.

Programs

Magma

[ n eq 0 select 1 else 3*5^(n-1): n in [0..20] ]; // Klaus Brockhaus, Apr 04 2010

Mathematica

CoefficientList[Series[(1-2x)/(1-5x),{x,0,30}],x] (* or *) Join[{1}, NestList[5#&,3,29]]  (* Harvey P. Dale, Apr 25 2011 *)

PARI

x='x+O('x^50); Vec((1-2*x)/(1-5*x)) \\ G. C. Greubel, Sep 15 2017

Formula

Binomial transform of A122117. - Philippe Deléham, Oct 19 2006

a(0) = 1, a(n) = 3*5^(n-1) for n >= 1. - Philippe Deléham, Oct 19 2006

E.g.f.: (2 + 3*exp(5*x))/5. - Ilya Gutkovskiy, Aug 11 2016

Extensions

Wrong formula deleted by Klaus Brockhaus, Apr 04 2010