A218149 - OEIS

A218149

a(n) = 3^((6+5*n+n^3)/6).

1, 3, 9, 81, 6561, 14348907, 2541865828329, 109418989131512359209, 3433683820292512484657849089281, 235655016338368235499067731945871638181119123, 106111661199647248543687855752712667991103904330482569981872649

(list; graph; refs; listen; history; text; internal format)

OFFSET

-1,2

COMMENTS

a(n) = a(0) * product(i=1,2,...k)r(i)^C(n,i), C(n,i)=0 for all i > n.

Here, it is submitted a special case of the geometric-geometric sequence having finite ratios, that is, k consecutive rows of ratios, whose first terms are r(1), r(2), r(3),..., r(k), the last row (k-th row) being of a constant ratio, with k=3, a(0)=r(1)=r(2)=r(3)=3.

LINKS

Table of n, a(n) for n=-1..9.

FORMULA

a(n) = a(n-1)*(2^(1+n*(n-1)/2)), with a(0)=3

EXAMPLE

a(3) = 3^((6+5*3+3^3)/6) = 3^((6+15+27)/6) = 3^(48/6) = 3^8 = 6561.

PROG

(Maxima) A218149(n):=3^((6+5*n+n^3)/6)$

makelist(A218149(n), n, -1, 10); /* Martin Ettl, Oct 31 2012 */

(PARI) a(n)=3^(n*(5+n^2)/6+1) \\ Charles R Greathouse IV, Jan 06 2013

CROSSREFS

Cf. A006125.