login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261875 Decimal expansion of the coefficient 'gamma' (see formula) appearing in Otter's result concerning the asymptotics of T_n, the number of non-isomorphic rooted trees of order n. 0
2, 6, 8, 1, 1, 2, 8, 1, 4, 7, 2, 6, 7, 1, 1, 2, 2, 3, 8, 5, 7, 7, 3, 2, 8, 7, 8, 3, 7, 0, 3, 9, 3, 7, 0, 9, 3, 5, 4, 1, 7, 5, 3, 4, 7, 2, 0, 1, 1, 6, 1, 6, 6, 3, 5, 2, 7, 4, 9, 7, 0, 2, 5, 8, 8, 6, 4, 0, 2, 8, 4, 0, 3, 6, 5, 1, 6, 5, 3, 4, 5, 0, 6, 7, 2, 3, 9, 2, 0, 8, 5, 5, 8, 7, 7, 5, 9, 9, 1, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 296.

LINKS

Table of n, a(n) for n=1..100.

FORMULA

Lim_{n->infinity} T_n*n^(3/2)/alpha^n = (beta/(2 Pi))^(1/3) = (1/(4 Pi alpha))^(1/2)*gamma, where alpha is A051491 and beta is A086308.

gamma = 2^(2/3)*Pi^(1/6)*beta^(1/3)*sqrt(alpha).

EXAMPLE

2.68112814726711223857732878370393709354175347201161663527497...

MATHEMATICA

digits = 100; max = 250; Clear[s, a]; 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}]; APrime[x_] := Sum[k*a[k]*x^(k-1), {k, 0, max}]; eq = Log[c] == 1 + Sum[A[c^-k]/k, {k, 2, max}]; alpha = c /. FindRoot[eq, {c, 3}, WorkingPrecision -> digits+5]; beta = (1+Sum[APrime[alpha^(-k)]/alpha^k, {k, 2, max}])^(3/2)/Sqrt[2*Pi]; gamma = 2^(2/3)*Pi^(1/6)*beta^(1/3) * Sqrt[alpha]; RealDigits[gamma, 10, digits] // First

CROSSREFS

Cf. A000055, A000081, A051491, A086308, A187770.

Sequence in context: A155003 A327279 A021377 * A084686 A040164 A086353

Adjacent sequences:  A261872 A261873 A261874 * A261876 A261877 A261878

KEYWORD

cons,nonn

AUTHOR

Jean-Fran├žois Alcover, Sep 04 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 9 22:52 EDT 2020. Contains 336335 sequences. (Running on oeis4.)