A259405 Decimal expansion of a constant related to A259373.

9, 0, 8, 6, 6, 1, 6, 6, 7, 6, 4, 4, 4, 5, 4, 8, 9, 2, 5, 6, 6, 5, 8, 1, 1, 3, 7, 7, 0, 2, 1, 5, 9, 2, 7, 8, 1, 3, 6, 9, 4, 2, 2, 1, 3, 7, 2, 7, 3, 7, 0, 6, 6, 6, 5, 1, 1, 2, 3, 4, 2, 8, 3, 3, 9, 7, 2, 2, 6, 8, 6, 5, 0, 1, 5, 4, 3, 7, 0, 7, 5, 9, 1, 8, 2, 4, 8, 8, 2, 1, 6, 8, 5, 7, 2, 6, 5

Offset

0,1

Links

Table of n, a(n) for n=0..96.

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

Cf. A000041, A259373, A058694, A259314, A133018.

Sequence in context: A021528 A210973 A154185 * A340879 A086199 A167545

Adjacent sequences: A259402 A259403 A259404 * A259406 A259407 A259408

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 26 2015

Status

approved