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

%I #20 Jan 30 2014 06:33:24

%S 1,2,4,16,256,32768,67108864,4398046511104,18446744073709551616,

%T 9903520314283042199192993792,

%U 1361129467683753853853498429727072845824,95780971304118053647396689196894323976171195136475136

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

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

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

%p A218148:=n->2^((6 + 5*n + n^3)/6); seq(A218148(n), n=-1..10); # _Wesley Ivan Hurt_, Jan 28 2014

%t Table[2^((6 + 5*n + n^3)/6), {n, -1, 10}] (* _T. D. Noe_, Oct 23 2012 *)

%o (Maxima) A218148(n):= if n=0 then 2 else 2^((6+5*n+n^3)/6)$ makelist(A218148(n),n,0,30); /* _Martin Ettl_, Oct 24 2012 */

%Y Cf. A006125.

%K nonn

%O -1,2

%A _Mokhtar Mohamed_, Oct 22 2012