A255504 - OEIS

A255504

Decimal expansion of a constant related to A255322.

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

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

FORMULA

Equals limit n->infinity (Product_{k=0..n} (k^2)!) / (n^((2*n + 1)*(2*n^2 + 2*n + 3)/6) * (2*Pi)^(n/2) / exp(5*n^3/9 + n^2/2 + n)).

Equals sqrt(2*Pi) * exp(Zeta(3)/(2*Pi^2)) * Product_{n>=1} ((n^2)!/stirling(n^2)), where stirling(n^2) = sqrt(2*Pi) * n^(2*n^2+1) / exp(n^2) is the Stirling approximation of (n^2)!. - Vaclav Kotesovec, Apr 20 2016

EXAMPLE

3.048330306522348566911920417337613015885313475689049184525483697684834...

CROSSREFS

Cf. A255322, A255511, A255438, A255439.

Cf. A074962, A243262, A243263, A243264, A243265.

Sequence in context: A303274 A199608 A128178 * A178593 A021332 A008344

Adjacent sequences: A255501 A255502 A255503 * A255505 A255506 A255507

KEYWORD

nonn,cons

AUTHOR

Vaclav Kotesovec, Feb 24 2015

STATUS

approved