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

Author

Jean-François Alcover, Jun 04 2014

Keywords

• nonn
• cons

Examples

			0.46563864677907573710997591026429...
		

References

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

Crossrefs

Cf. A038037, A242769, A243395.

Programs

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

Formula

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