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

Author

David Broadhurst

Keywords

• nonn
• nice
• cons

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

Examples

			2.95576528565199497471481752412319458837549230466359659535...
		

References

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

Links

• David Broadhurst, Resurgent Integer Sequences, Rutgers Experimental Math Seminar, Feb 06 2025; Slides.
• 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

Crossrefs

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

Programs

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 *)