OFFSET
0,1
COMMENTS
The article "Acyclic digraphs and eigenvalues of (0,1)-matrices" gives the wrong value M=0.474! See A003024 for more. - Vaclav Kotesovec, Jul 28 2014
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 310.
LINKS
B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices, J. Integer Sequences, 7 (2004), #04.3.3.
B. D. McKay, F. E. Oggier, G. F. Royle, N. J. A. Sloane, I. M. Wanless and H. S. Wilf, Acyclic digraphs and eigenvalues of (0,1)-matrices, arXiv:math.CO/0310423 (2003)
FORMULA
eta_A = xi_A*lambda(xi_A/2), where xi_A is the smallest positive root of lambda(x) = sum_{n >= 0} (-1)^n*x^n/(2^(n*(n-1)/2)*n!).
EXAMPLE
0.5743623733093114769166708016815072469721884609708754240690224791220286894...
MATHEMATICA
digits = 103; lambda[x_?NumericQ] := NSum[(-1)^n*x^n/(2^(n*(n - 1)/2)*n!), {n, 0, Infinity}, WorkingPrecision -> digits + 10, Method -> "AlternatingSigns"]; xi = x /. FindRoot[lambda[x] == 0, {x, 3/2}, WorkingPrecision -> digits + 10]; RealDigits[xi*lambda[xi/2], 10, digits] // First
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Jul 28 2014
STATUS
approved