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 A245655 Decimal expansion of eta_A, a constant associated with the asymptotics of the enumeration of labeled acyclic digraphs. 0
 5, 7, 4, 3, 6, 2, 3, 7, 3, 3, 0, 9, 3, 1, 1, 4, 7, 6, 9, 1, 6, 6, 7, 0, 8, 0, 1, 6, 8, 1, 5, 0, 7, 2, 4, 6, 9, 7, 2, 1, 8, 8, 4, 6, 0, 9, 7, 0, 8, 7, 5, 4, 2, 4, 0, 6, 9, 0, 2, 2, 4, 7, 9, 1, 2, 2, 0, 2, 8, 6, 8, 9, 4, 0, 3, 7, 1, 7, 7, 3, 3, 7, 7, 1, 5, 7, 3, 8, 0, 5, 2, 5, 3, 5, 4, 1, 0, 6, 4, 2, 6, 9, 4 (list; constant; graph; refs; listen; history; text; internal format)
 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 Cf. A245654, A003024. Sequence in context: A258162 A021868 A243395 * A011497 A010488 A300081 Adjacent sequences:  A245652 A245653 A245654 * A245656 A245657 A245658 KEYWORD nonn,cons AUTHOR Jean-François Alcover, Jul 28 2014 STATUS approved

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Last modified June 23 23:39 EDT 2021. Contains 345403 sequences. (Running on oeis4.)