A158621 Partial products of A001093.

9, 252, 16380, 2063880, 447861960, 154064514240, 79035095805120, 57695619937737600, 57753315557675337600, 76927416322823549683200, 133007502822161917402252800, 292350491203111894450151654400

Offset: 2

Author

Jonathan Vos Post, Mar 23 2009

Keywords

• easy
• nonn

Comments

A158620(n) = PRODUCT[k=2..n](k^3-1). A158622(n) is the numerator of the reduced fraction A158620(n)/A158621(n). A158623(n) is the denominator of the reduced fraction A158620(n)/A158621(n).

Examples

			a(2) = 2^3+1 = 9. a(3) = (2^3+1)*(3^3+1) = 9 * 28 = 252. a(4) = (2^3+1)*(3^3+1)*(4^3+1) = 9 * 28 * 65 = 16380.
		

Crossrefs

Cf. A001093, A016921, A068601, A158620, A158622-A158624, A255433.

Programs

Mathematica

Table[Product[(k^3+1),{k,2,n}],{n,2,20}] (* Vaclav Kotesovec, Jul 11 2015 *)
FoldList[Times,Range[2,20]^3+1] (* Harvey P. Dale, Oct 15 2017 *)

Formula

PRODUCT[k=2..n](k^3+1) = PRODUCT[k=2..n]A001093(k).

a(n) ~ sqrt(2*Pi) * cosh(sqrt(3)*Pi/2) * n^(3*n+3/2) / exp(3*n). - Vaclav Kotesovec, Jul 11 2015