A067623 Consider the power series (x+1)^(1/3)=1+x/3-x^2/9+5x^3/81+...; sequence gives denominators of coefficients.

1, 3, 9, 81, 243, 729, 6561, 19683, 59049, 1594323, 4782969, 14348907, 129140163, 387420489, 1162261467, 10460353203, 31381059609, 94143178827, 2541865828329, 7625597484987, 22876792454961, 205891132094649, 617673396283947

Offset: 0

Author

Benoit Cloitre, Feb 02 2002

Keywords

• nonn
• frac

Comments

All terms are powers of 3.

Crossrefs

Cf. A004128, A046161, A067622 (numerators), A123854.

Programs

Maple

A067623 := n -> denom(binomial(1/3,n)):
seq(A067623(n), n=0..21); # Peter Luschny, Apr 07 2016

Mathematica

Table[Denominator@ Binomial[1/3, n], {n, 0, 22}] (* Michael De Vlieger, Apr 07 2016 *)

Formula

a(n) = 3^A004128(n).

a(n) = 3^n*a(floor(n/3)). - Vladeta Jovovic, Mar 01 2004

a(n) = denominator(binomial(1/3, n)). - Peter Luschny, Apr 07 2016