A051491 Decimal expansion of Otter's rooted tree constant: lim_{n->inf} A000081(n+1)/A000081(n).

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

Offset

1,1

Comments

A000055(n) ~ A086308 * A051491^n * n^(-5/2), A000081(n) ~ A187770 * A051491^n * n^(-3/2). - Vaclav Kotesovec, Jan 04 2013

Analytic Combinatorics (Flajolet and Sedgewick, 2009, p. 481) has a wrong value of this constant (2.9955765856). - Vaclav Kotesovec, Jan 04 2013

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 295-316.

Links

Table of n, a(n) for n=1..102.

Amirmohammad Farzaneh, Mihai-Alin Badiu, and Justin P. Coon, On Random Tree Structures, Their Entropy, and Compression, arXiv:2309.09779 [cs.IT], 2023.

S. R. Finch, Otter's Tree Enumeration Constants [Broken link]

S. R. Finch, Otter's Tree Enumeration Constants [Wayback Machine]

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009, p. 481

Simon Plouffe, Tree-growth constant to 1800 digits

Eric Weisstein's World of Mathematics, Rooted Tree

Eric Weisstein's World of Mathematics, Tree

Index entries for sequences related to trees

Index entries for sequences related to rooted trees

Example

2.95576528565199497471481752412319458837549230466359659535...

Mathematica

digits = 99; max = 250; s[n_, k_] := s[n, k] = a[n+1-k] + If[n < 2*k, 0, s[n-k, k]]; a[1] = 1; a[n_] := a[n] = Sum[a[k]*s[n-1, k]*k, {k, 1, n-1}]/(n-1); A[x_] := Sum[a[k]*x^k, {k, 0, max}]; eq = Log[c] == 1+Sum[A[c^-k]/k, {k, 2, max}]; alpha = c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits+5]; RealDigits[alpha, 10, digits] // First (* Jean-François Alcover, Sep 24 2014 *)

Crossrefs

Cf. A000081, A051492, A187770, A000055, A086308, A215978, A274082.

Sequence in context: A019708 A201397 A077124 * A339204 A253169 A339925

Adjacent sequences: A051488 A051489 A051490 * A051492 A051493 A051494

Keyword

nonn,nice,cons

Author

David Broadhurst

Status

approved