OFFSET
1,2
REFERENCES
S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.7.
R. W. Robinson, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1980.
LINKS
R. W. Robinson, Table of n, a(n) for n = 1..190
Phil Hanlon, Counting interval graphs, Trans. Amer. Math. Soc. 272 (1982), no. 2, 383-426.
FORMULA
G.f. A(x) = x + 2x^2 + 4x^3 + 9x^4 + 21x^5 + ... satisfies 1 + A(x) = exp( Sum_{k >= 1} psi(x^k)/k ), where psi(x) = (1+2*x-sqrt(1-4*x)*sqrt(1-4*x^2))/(4*sqrt(1-4*x^2)) is the g.f. for A007123.
For asymptotics, see for example Finch.
MATHEMATICA
m = 30;
A[x_] = (-1 + Exp[Sum[psi[x^k]/k, {k, 1, m}]] /. psi[x_] -> (1 + 2 x - Sqrt[1 - 4 x] Sqrt[1 - 4 x^2])/(4 Sqrt[1 - 4 x^2])) + O[x]^m;
CoefficientList[A[x], x] // Rest (* Jean-François Alcover, Oct 24 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved