A259314 Decimal expansion of partition factorial constant.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Vaclav Kotesovec, The partition factorial constant and asymptotics of the sequence A058694

Formula

Equals limit n->infinity Product_{k=1..n} p(k) / (exp(Pi*sqrt(2/3*(k-1/24))) / (4*sqrt(3)*(k-1/24)) * (1 - sqrt(3/(2*(k-1/24)))/Pi)), where p(k) is the partition function A000041.

Example

0.91101673133224995186154746959468345278073860978008093028132149022759...

Mathematica

(* The iteration cycle: *) Do[Print[Product[N[PartitionsP[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))), 150], {k, 1, n}]], {n, 500, 50000, 500}]

Crossrefs

Cf. A000041, A058694, A062073, A218490, A253924, A256831, A259405.

Sequence in context: A081801 A176522 A219732 * A266557 A010534 A078297

Adjacent sequences: A259311 A259312 A259313 * A259315 A259316 A259317

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 24 2015

Status

approved