A158621 Partial products of A001093.

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).

Links

Table of n, a(n) for n=2..13.

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 *)

Crossrefs

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

Sequence in context: A303050 A194790 A370357 * A256019 A135484 A345160

Adjacent sequences: A158618 A158619 A158620 * A158622 A158623 A158624

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 23 2009

Status

approved