OFFSET
2,1
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
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..180
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
EXAMPLE
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.
MATHEMATICA
Rest[FoldList[Times, 1, Range[2, 15]^3-1]] (* Harvey P. Dale, Apr 18 2015 *)
PROG
(PARI) a(n) = prod(k = 2, n, k^3 - 1); \\ Michel Marcus, Sep 29 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 23 2009
STATUS
approved