A158620 Partial products of A068601.

7, 182, 11466, 1421784, 305683560, 104543777520, 53421870312720, 38891121587660160, 38852230466072499840, 51673466519876424787200, 89240076679826585607494400, 195971208388899181994057702400

Offset: 2

Author

Jonathan Vos Post, Mar 23 2009

Keywords

• easy
• nonn

Comments

A158621(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).

Also the determinant of the n X n matrix given by m(i,j) = i^3 if i=j and 1 otherwise. For example, Det[{{1,1,1, 1},{1,8,1,1},{1,1,27,1},{1,1,1,64}}] = 11466 = a(4). - John M. Campbell, May 20 2011

Examples

			a(2) = 2^3-1 = 7.
a(3) = (2^3-1)*(3^3-1) = 7 * 26 = 182.
a(4) = (2^3-1)*(3^3-1)*(4^3-1) = 7 * 26 * 63 = 11466.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 2..180

Crossrefs

Cf. A000217, A005448, A016921, A068601, A158621-A158624, A010791.

Programs

Mathematica

Rest[FoldList[Times,1,Range[2,15]^3-1]] (* Harvey P. Dale, Apr 18 2015 *)

PARI

a(n) = prod(k = 2, n, k^3 - 1); \\ Michel Marcus, Sep 29 2013

Formula

Product_{k=2..n} (k^3-1) = Product_{k=2..n} A068601(k).

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