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

Author

Eric W. Weisstein, Jul 15 2003

Keywords

• nonn
• cons

Examples

			0.791603183577511807823628455723268224071742418090789...
		

References

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

Links

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

Crossrefs

Cf. A001190, A086317.

Programs

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 *)

Formula

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