A158621 - OEIS

%I #9 Oct 15 2017 11:58:44

%S 9,252,16380,2063880,447861960,154064514240,79035095805120,

%T 57695619937737600,57753315557675337600,76927416322823549683200,

%U 133007502822161917402252800,292350491203111894450151654400

%N Partial products of A001093.

%C 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).

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

%F a(n) ~ sqrt(2*Pi) * cosh(sqrt(3)*Pi/2) * n^(3*n+3/2) / exp(3*n). - _Vaclav Kotesovec_, Jul 11 2015

%e 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.

%t Table[Product[(k^3+1),{k,2,n}],{n,2,20}] (* _Vaclav Kotesovec_, Jul 11 2015 *)

%t FoldList[Times,Range[2,20]^3+1] (* _Harvey P. Dale_, Oct 15 2017 *)

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

%K easy,nonn

%O 2,1

%A _Jonathan Vos Post_, Mar 23 2009