A367842 - OEIS

A367842

Decimal expansion of limit_{n->oo} Product_{k=1..n} Gamma(k/n)^(k/n^2).

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

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OFFSET

1,2

COMMENTS

Limit_{n->oo} Product_{k=1..n} Gamma(k/n)^(1/n) = sqrt(2*Pi).

LINKS

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

FORMULA

Equals (2*Pi)^(1/4) / A, where A = A074962 is the Glaisher-Kinkelin constant.

Equals A010767 * A092040 / A074962.

Equals exp(Integral_{x=0..1} x*log(Gamma(x)) dx).

EXAMPLE