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A249185 Decimal expansion of a constant appearing in the Hankel determinant asymptotics. 1
6, 4, 5, 0, 0, 2, 4, 4, 8, 5, 0, 9, 5, 7, 7, 0, 8, 4, 6, 5, 8, 9, 6, 1, 0, 0, 7, 7, 2, 1, 7, 8, 7, 6, 5, 5, 3, 4, 7, 6, 1, 4, 4, 9, 4, 0, 5, 7, 3, 3, 9, 7, 2, 1, 5, 5, 2, 1, 4, 4, 5, 8, 8, 5, 8, 0, 2, 7, 6, 0, 7, 8, 7, 4, 1, 2, 4, 6, 8, 4, 6, 5, 7, 3, 9, 7, 1, 0, 5, 4, 9, 7, 1, 9, 7, 4, 0, 9, 9, 1, 4, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..101.

Steven Finch, Hankel and Toeplitz Determinants, March 17, 2014. [Cached copy, with permission of the author]

Eric Weisstein's MathWorld, Hilbert matrix

Wikipedia, Hilbert matrix

FORMULA

Det(H_n) ~ h*4^(-n^2)*(2*Pi)^n*n^(-1/4), where h = 2^(1/12)*e^(1/4)*A^(-3), A denoting the Glaisher-Kinkelin constant.

EXAMPLE

0.645002448509577084658961007721787655347614494...

MAPLE

evalf(limit(2^(1/12) * n^(3*n^2/2 + 3*n/2 + 1/4) * exp(1/4-3*n^2/4) / product(k^(3*k), k=1..n), n=infinity), 120); # Vaclav Kotesovec, Oct 23 2014

MATHEMATICA

h = 2^(1/12)*E^(1/4)*Glaisher^-3; RealDigits[h, 10, 102] // First

CROSSREFS

Cf. A005249, A074962.

Sequence in context: A019174 A019166 A058158 * A021159 A106332 A247319

Adjacent sequences:  A249182 A249183 A249184 * A249186 A249187 A249188

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Oct 23 2014

STATUS

approved

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Last modified July 20 01:17 EDT 2019. Contains 325168 sequences. (Running on oeis4.)