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a(n) = Product_{k=1..n} d(2*k), where d() is the number of divisors function A000005.
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%I #17 May 29 2020 02:22:04

%S 2,6,24,96,384,2304,9216,46080,276480,1658880,6635520,53084160,

%T 212336640,1274019840,10192158720,61152952320,244611809280,

%U 2201506283520,8806025134080,70448201072640,563585608581120,3381513651486720,13526054605946880

%N a(n) = Product_{k=1..n} d(2*k), where d() is the number of divisors function A000005.

%e a(4) = d(2)*d(4)*d(6)*d(8) = 2*3*4*4 = 96.

%t Rest @ FoldList[Times, 1, DivisorSigma[0, Range[2, 40, 2]]] (* _Amiram Eldar_, May 10 2020 *)

%o (PARI) a(n) = prod(k=1, n, numdiv(2*k)); \\ _Michel Marcus_, May 10 2020

%Y Cf. A000005, A066843, A099777.

%K nonn

%O 1,1

%A _Ctibor O. Zizka_, May 10 2020