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A259314 Decimal expansion of partition factorial constant. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 11:01 EST 2020. Contains 331105 sequences. (Running on oeis4.)