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A259314 Decimal expansion of partition factorial constant. 4

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of partition factorial constant.

%H Vaclav Kotesovec, <a href="http://oeis.org/A058694/a058694_2.pdf">The partition factorial constant and asymptotics of the sequence A058694</a>

%F 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.

%e 0.91101673133224995186154746959468345278073860978008093028132149022759...

%t (* 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}]

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

%K nonn,cons

%O 0,1

%A _Vaclav Kotesovec_, Jun 24 2015

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Last modified February 20 19:36 EST 2020. Contains 332084 sequences. (Running on oeis4.)