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%I #19 Feb 01 2017 12:29:22
%S 7,182,11466,1421784,305683560,104543777520,53421870312720,
%T 38891121587660160,38852230466072499840,51673466519876424787200,
%U 89240076679826585607494400,195971208388899181994057702400
%N Partial products of A068601.
%C 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).
%C 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
%H G. C. Greubel, <a href="/A158620/b158620.txt">Table of n, a(n) for n = 2..180</a>
%F Product_{k=2..n} (k^3-1) = Product_{k=2..n} A068601(k).
%F 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
%e a(2) = 2^3-1 = 7.
%e a(3) = (2^3-1)*(3^3-1) = 7 * 26 = 182.
%e a(4) = (2^3-1)*(3^3-1)*(4^3-1) = 7 * 26 * 63 = 11466.
%t Rest[FoldList[Times,1,Range[2,15]^3-1]] (* _Harvey P. Dale_, Apr 18 2015 *)
%o (PARI) a(n) = prod(k = 2, n, k^3 - 1); \\ _Michel Marcus_, Sep 29 2013
%Y Cf. A000217, A005448, A016921, A068601, A158621-A158624, A010791.
%K easy,nonn
%O 2,1
%A _Jonathan Vos Post_, Mar 23 2009
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