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a(n) = 3^((6+5*n+n^3)/6).
2

%I #14 Feb 27 2013 09:48:51

%S 1,3,9,81,6561,14348907,2541865828329,109418989131512359209,

%T 3433683820292512484657849089281,

%U 235655016338368235499067731945871638181119123,106111661199647248543687855752712667991103904330482569981872649

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

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

%C 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.

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

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

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

%o makelist(A218149(n),n,-1,10); /* _Martin Ettl_, Oct 31 2012 */

%o (PARI) a(n)=3^(n*(5+n^2)/6+1) \\ _Charles R Greathouse IV_, Jan 06 2013

%Y Cf. A006125.

%K nonn,easy

%O -1,2

%A _Mokhtar Mohamed_, Oct 22 2012