OFFSET
1,4
REFERENCES
F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 31, problem 1.16(a).
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..50
Marko R. Riedel, Geoffrey Critzer, Math.Stackexchange.com, Proof of the closed form of the e.g.f. by combinatorial species.
FORMULA
E.g.f.: (z^2/(1-z))*(A'(z)-A(z)) where A(z) = exp(1/2*z^2) * Sum_{n>=0}(2^binomial(n, 2)*(z/exp(z))^n/n!).
MAPLE
MX := 16:
XGF := exp(z^2/2)*add((z/exp(z))^n*2^binomial(n, 2)/n!, n=0..MX+5):
K1 := z^2/(1-z)*(diff(XGF, z)-XGF):
XS := series(K1, z=0, MX+1):
seq(n!*coeff(XS, z, n), n=1..MX);
MATHEMATICA
m = 16;
A[z_] := Exp[1/2*z^2]*Sum[2^Binomial[n, 2]*(z/Exp[z])^n/n!, {n, 0, m}];
egf = (z^2/(1 - z))*(A'[z] - A[z]);
a[n_] := SeriesCoefficient[egf, {z, 0, n}]*n!;
Array[a, m] (* Jean-François Alcover, Feb 23 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Riedel, Sep 27 2016
STATUS
approved