A086318 Decimal expansion of asymptotic constant eta for counts of weakly binary trees.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.6, p. 297.

Links

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Weakly binary tree.

Formula

Equals lim_{n->oo} A001190(n)*n^(3/2)/A086317^(n-1). - Vaclav Kotesovec, Apr 19 2016

Example

0.791603183577511807823628455723268224071742418090789...

Mathematica

digits = 102; c[0] = 2; c[n_] := c[n] = c[n - 1]^2 + 2; eta[n_Integer] := eta[n] = 1/2 * Sqrt[c[n]^2^(-n)/Pi] * Sqrt[3 + Sum[1/Product[c[j], {j, 1, k}], {k, 1, n}]]; eta[5]; eta[n = 10]; While[RealDigits[eta[n], 10, digits] != RealDigits[eta[n - 5], 10, digits], n = n + 5]; RealDigits[eta[n], 10, digits] // First (* Jean-François Alcover, May 27 2014 *)

Crossrefs

Cf. A001190, A086317.

Sequence in context: A091900 A222135 A377622 * A244674 A130834 A132806

Adjacent sequences: A086315 A086316 A086317 * A086319 A086320 A086321

Keyword

nonn,cons,changed

Author

Eric W. Weisstein, Jul 15 2003

Status

approved