A246949 Decimal expansion of the coefficient K appearing in the asymptotic expression of the number of forests of ordered trees on n total nodes as K*4^(n-1)/sqrt(Pi*n^3).

1, 7, 1, 6, 0, 3, 0, 5, 3, 4, 9, 2, 2, 2, 8, 1, 9, 6, 4, 0, 4, 7, 4, 6, 4, 3, 9, 9, 0, 4, 2, 2, 1, 2, 0, 9, 1, 9, 6, 9, 7, 6, 7, 8, 3, 7, 3, 1, 7, 8, 6, 3, 4, 6, 3, 1, 8, 6, 8, 1, 9, 4, 0, 7, 1, 4, 5, 1, 4, 9, 6, 2, 1, 3, 2, 6, 0, 2, 0, 1, 6, 9, 3, 6, 6, 4, 2, 7, 2, 3, 8, 1, 5, 2, 6, 4, 6, 1, 1, 7, 3, 0, 1, 1, 5

Offset

1,2

Comments

See A052854.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 45.

Ph. Flajolet, É. Fusy, X. Gourdon, D. Panario, N. Pouyanne, A Hybrid of Darboux's Method and Singularity Analysis in Combinatorial Asymptotics, arXiv:math/0606370 [math.CO], 2006.

Formula

exp(sum_{k>=1} 1/(2*k)*(1 - sqrt(1 - 4^(1 - k))).

Example

1.7160305349222819640474643990422120919697678373178634631868194...

Maple

evalf(exp(sum(1/(2*k)*(1-sqrt(1-4^(1-k))), k=1..infinity)), 100); # Vaclav Kotesovec, Sep 17 2014

Mathematica

digits = 76; K = Exp[NSum[1/(2 k)*(1 - Sqrt[1 - 4^(1 - k)]), {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 100]]; RealDigits[K, 10, digits] // First

Crossrefs

Cf. A052854.

Sequence in context: A064467 A089204 A107786 * A154932 A026497 A010146

Adjacent sequences: A246946 A246947 A246948 * A246950 A246951 A246952

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 08 2014

Extensions

More terms from Vaclav Kotesovec, Sep 17 2014

Status

approved