OFFSET
0,4
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 306, (4.2.35).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 73, (3.4.21).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1 (1992) pp. 53-80.
P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)
FORMULA
a(n)=b(2n+1). A003080(n)=c(2n+1).
G.f.: B(x)=C(x)+(C(x^3)-C(x)^3)/3.
G.f.: g(x) + x*(g(x^3) - g(x)^3)/3 where g(x) is the g.f. of A003080. - Andrew Howroyd, Feb 18 2020
MATHEMATICA
terms = 31;
nmax = 2 terms;
A[_] = 0;
Do[A[x_] = x Exp[Sum[(A[x^n]^2 + A[x^(2n)])/(2n), {n, 1, terms}]] + O[x]^nmax // Normal, {nmax}];
g[x_] = (A[x] /. x^k_ -> x^((k - 1)/2)) - x + 1;
g[x] + x((g[x^3] - g[x]^3)/3) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2020, after Andrew Howroyd *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Extended with formula by Christian G. Bower, 10/98
STATUS
approved