OFFSET
0,1
FORMULA
Equals limit n->infinity Product_{k=1..n} p(k)^k / (exp(Pi*sqrt(2/3*(k-1/24))) / (4*sqrt(3)*(k-1/24)) * (1 - sqrt(3/(2*(k-1/24)))/Pi))^k, where p(k) is the partition function A000041.
EXAMPLE
0.908661667644454892566581137702159278136942213727370666511234283397226865...
MATHEMATICA
(* The iteration cycle: *) Do[Print[Product[N[PartitionsP[k]^k/((E^(Sqrt[2/3]*Sqrt[k-1/24]*Pi) * (1 - Sqrt[3/2]/(Sqrt[k-1/24]*Pi))) / (4*Sqrt[3]*(k-1/24)))^k, 150], {k, 1, n}]], {n, 1000, 50000, 1000}]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jun 26 2015
STATUS
approved