login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007106 Number of labeled odd degree trees with 2n nodes.
(Formerly M3704)
8
1, 4, 96, 5888, 686080, 130179072, 36590059520, 14290429935616, 7405376630685696, 4917457306800619520, 4071967909087792857088, 4113850542422629363482624, 4980673081258443273955966976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

R. W. Robinson, personal communication.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. W. Robinson, Table of n, a(n) for n = 1..39

B. R. Jones, On tree hook length formulas, Feynman rules and B-series, Master's thesis, Simon Fraser University, 2014.

Math.Stackexchange.Com, Marko R. Riedel, Odd degree trees

Marko Riedel, Maple code for species based enumeration, closed form and total enumeration.

Index entries for sequences related to trees

FORMULA

a(n) = A060279(n)/(2*n). - Vladeta Jovovic, Feb 08 2005

Bisection of A058014. The expansion 1/sqrt(1+x^2)*arcsinh(x) = x - 4*x^3/3! + 64*x^5/5! - ... (see A002454) has series reversion x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + .... The coefficients appear to be the terms of this sequence. As an x-adic limit this e.g.f. equals lim {n -> inf} sinh(f(n,x)), where f(0,x) = x and f(n,x) = x*cosh(f(n-1,x)) for n >= 1. See the example section below. - Peter Bala, Apr 24 2012

a(n) = Sum_{k=1..n} C(n,k) * k! * (n-2)! [z^{n-2}] [u^k] exp(u(exp(z)+exp(-z)-2)/2)), -Marko Riedel, Jun 16 2016

EXAMPLE

From Peter Bala, Apr 24 2012: (Start)

Let G(x) = 1 + x^2/2! + 13*x^4/4! + 541*x^6/6! + ... be the e.g.f. for A143601. Then sinh(x*G(x)) = x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + ....

Conjectural e.g.f. as an x-adic limit:

sinh(x) = x + ...; sinh(x*cosh(x)) = x + 4*x^3/3! + ...;

sinh(x*cosh(x*cosh(x))) = x + 4*x^3/3! + 96*x^5/5! + ...;

sinh(x*cosh(x*cosh(x*cosh(x)))) = x + 4*x^3/3! + 96*x^5/5! + 5888*x^7/7! + ....

(End)

MAPLE

A007106(n) = A(2n) where n>=2, A(n) = (add(binomial(n, q)*(n-2*q)^(n-2)/(n-2)!, q=0..n) - add(binomial(n-1, q)*(n-2*q)^(n-3)/(n-3)!, q=0..n-1) + add(binomial(n-1, q)*(n-2-2*q)^(n-3)/(n-3)!, q=0..n-1))*n!/2^(n+1)/(n-1)

CROSSREFS

Cf. A058014, A143601.

Sequence in context: A013042 A190196 A065140 * A111637 A027872 A308146

Adjacent sequences:  A007103 A007104 A007105 * A007107 A007108 A007109

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended by Vladeta Jovovic, Feb 08 2005

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 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)