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A259405 Decimal expansion of a constant related to A259373. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A086199 A167545 A272965

Adjacent sequences:  A259402 A259403 A259404 * A259406 A259407 A259408

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Jun 26 2015

STATUS

approved

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Last modified February 24 06:13 EST 2020. Contains 332199 sequences. (Running on oeis4.)