<s>
The	O
coefficients	O
of	O
Faulhaber	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
in	O
its	O
general	O
form	O
involve	O
the	O
Bernoulli	O
numbers	O
Bj	O
.	O
</s>
<s>
Faulhaber	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
is	O
also	O
called	O
Bernoulli	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
.	O
</s>
<s>
Rather	O
,	O
he	O
knew	O
at	O
least	O
the	O
first	O
17	O
cases	O
,	O
as	O
well	O
as	O
the	O
existence	O
of	O
the	O
Faulhaber	B-Algorithm
polynomials	I-Algorithm
for	O
odd	O
powers	O
described	O
below	O
.	O
</s>
<s>
The	O
term	O
Faulhaber	B-Algorithm
polynomials	I-Algorithm
is	O
used	O
by	O
some	O
authors	O
to	O
refer	O
to	O
another	O
polynomial	O
sequence	O
related	O
to	O
that	O
given	O
above	O
.	O
</s>
<s>
Some	O
authors	O
call	O
the	O
polynomials	O
in	O
a	O
on	O
the	O
right-hand	O
sides	O
of	O
these	O
identities	O
Faulhaber	B-Algorithm
polynomials	I-Algorithm
.	O
</s>
<s>
Faulhaber	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
can	O
also	O
be	O
written	O
in	O
a	O
form	O
using	O
matrix	O
multiplication	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
expressed	O
in	O
terms	O
of	O
Stirling	O
numbers	O
of	O
the	O
second	O
kind	O
and	O
falling	O
factorials	O
as	O
This	O
is	O
due	O
to	O
the	O
definition	O
of	O
the	O
Stirling	O
numbers	O
of	O
the	O
second	O
kind	O
as	O
mononomials	O
in	O
terms	O
of	O
falling	O
factorials	O
,	O
and	O
the	O
behaviour	O
of	O
falling	O
factorials	O
under	O
the	O
indefinite	B-Algorithm
sum	I-Algorithm
.	O
</s>
<s>
Faulhaber	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
was	O
generalized	O
by	O
Guo	O
and	O
Zeng	O
to	O
a	O
-analog	O
.	O
</s>
<s>
A	O
derivation	O
of	O
Faulhaber	B-Algorithm
's	I-Algorithm
formula	I-Algorithm
using	O
the	O
umbral	O
form	O
is	O
available	O
in	O
The	O
Book	O
of	O
Numbers	O
by	O
John	O
Horton	O
Conway	O
and	O
Richard	O
K	O
.	O
Guy	O
.	O
</s>
