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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

Table of n, a(n) for n=0..102.

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-Fran├žois Alcover, Jul 28 2014

STATUS

approved

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