A086318 - OEIS

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

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OFFSET

0,1

LINKS

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

Eric Weisstein's World of Mathematics, Weakly binary tree

FORMULA

Equals lim n -> infinity 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: A175638 A091900 A222135 * A244674 A130834 A132806

Adjacent sequences: A086315 A086316 A086317 * A086319 A086320 A086321

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Jul 15 2003

STATUS

approved