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A086318 Decimal expansion of asymptotic constant eta for counts of weakly binary trees. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 24 04:14 EDT 2017. Contains 292402 sequences.