A243396 Decimal expansion of 'etaHat', a constant used in the asymptotic evaluation of e.g.f. coefficients for the number of labeled mobiles.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 303.

Links

Table of n, a(n) for n=0..103.

Formula

A038037 = Numerator of n-th coefficient ~ etaHat * xiHat^n * n^(n-1), where xiHat is A243395.

Example

0.46563864677907573710997591026429...

Mathematica

digits = 104; mu = x /. FindRoot[x/(1 - x) == 1 + Log[1/(1 - x)], {x, 1/2}, WorkingPrecision -> digits + 5] ; etaHat = Sqrt[mu*(1 - mu)]; RealDigits[etaHat, 10, digits] // First

Crossrefs

Cf. A038037, A242769, A243395.

Sequence in context: A088559 A092526 A307463 * A140243 A366872 A343470

Adjacent sequences: A243393 A243394 A243395 * A243397 A243398 A243399

Keyword

nonn,cons

Author

Jean-François Alcover, Jun 04 2014

Status

approved