A245655 Decimal expansion of eta_A, a constant associated with the asymptotics of the enumeration of labeled acyclic digraphs.

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

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-François Alcover, Jul 28 2014

Status

approved