cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A259314 Decimal expansion of partition factorial constant.

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%I A259314 #14 Jun 26 2015 18:26:16
%S A259314 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 A259314 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 A259314 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 A259314 Decimal expansion of partition factorial constant.
%H A259314 Vaclav Kotesovec, <a href="http://oeis.org/A058694/a058694_2.pdf">The partition factorial constant and asymptotics of the sequence A058694</a>
%F A259314 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 A259314 0.91101673133224995186154746959468345278073860978008093028132149022759...
%t A259314 (* 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 A259314 Cf. A000041, A058694, A062073, A218490, A253924, A256831, A259405.
%K A259314 nonn,cons
%O A259314 0,1
%A A259314 _Vaclav Kotesovec_, Jun 24 2015