Abstract
Let
Φ
(
u
,
v
)
=
∑
m
=
0
∞
∑
n
=
0
∞
c
mn
u
m
v
n
. Bouwkamp and de Bruijn found that there exists a power series
Ψ
(
u
,
v
)
satisfying the equation
t
Ψ
(
tz
,
z
)
=
log
∑
k
=
0
∞
t
k
k
!
exp
(
k
Φ
(
kz
,
z
)
)
. We show that this result can be interpreted combinatorially using hypergraphs. We also explain some facts about
Φ
(
u
,
0
)
and
Ψ
(
u
,
0
)
, shown by Bouwkamp and de Bruijn, by using hypertrees, and we use Lagrange inversion to count hypertrees by number of vertices and number of edges of a specified size.