A181335 Partial products of A036691.

1, 4, 96, 18432, 31850496, 550376570880, 114126085737676800, 331312591939905257472000, 14427205603578338379772723200000, 10051861189298894268003697526046720000000

Offset: 0

Author

Jonathan Vos Post, Jan 28 2011

Keywords

• nonn
• easy

Comments

Product of the first n compositorial numbers (which are themselves the product of the first n composite numbers). This is to compositorial numbers (A036691), as superfactorials (A000178) are to factorials (A000142).

Examples

			a(3) = 1 * 4 * 24 * 192 = (1) * (1*4) * (1*4*6) * (1*4*6*8), since the first 4 composite numbers are (4, 6, 8) and the 0th compositorial is 1.
		

Crossrefs

Cf. A000142, A000178, A002808, A036691.

Programs

Mathematica

nn=20;cnos=Complement[Range[nn],Prime[Range[PrimePi[nn]]]];Rest[ FoldList[ Times,1,Rest[FoldList[Times,1,cnos]]]] (* Harvey P. Dale, Jun 28 2011 *)

Formula

a(n) = Product_{i=0..n} A036691(i) = Product_{i=0..n} Product_{j=1..i} A002808(j).