A218151 - OEIS

%I #16 Apr 20 2024 13:40:54

%S 2,6,90,6750,2531250,4746093750,44494628906250,2085685729980468750,

%T 488832592964172363281250,572850694879889488220214843750,

%U 3356547040311852470040321350097656250,98336339071636302833212539553642272949218750

%N a(n) = 2*3^n*5^(n*(n-1)/2).

%C a(n) = a(0)*Product_{i = 1..k} r(i)^C(n,i), with C(n,i) = 0 for all i > n. This is 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 = 2, a(0) = 2, r(1) = 3, r(2) = 5.

%F a(n) = a(n-1)*3*5^(n-1), a(0) = 2.

%e a(3) = 6750 because a(3) = 2*3^3*5^(3*2/2) = 2*3^3*5^3 = 2*27*125 = 6750.

%t RecurrenceTable[{a[0]==2,a[n]==a[n-1]3*5^(n-1)},a,{n,20}] (* _Harvey P. Dale_, Jul 30 2019 *)

%o (Maxima) A218151(n):=2*3^n*5^(n*(n-1)/2)$

%o makelist(A218151(n),n,0,11); /* _Martin Ettl_, Nov 03 2012 */

%Y Cf. A218148, A218149, A218150.

%K nonn

%O 0,1

%A _Mokhtar Mohamed_, Oct 23 2012