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A158621
Partial products of A001093.
6
9, 252, 16380, 2063880, 447861960, 154064514240, 79035095805120, 57695619937737600, 57753315557675337600, 76927416322823549683200, 133007502822161917402252800, 292350491203111894450151654400
OFFSET
2,1
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).
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
EXAMPLE
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.
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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Mar 23 2009
STATUS
approved