In this paper we present some new binomial identities for multiple harmonic sums whose indices are the sequences
(
{
1
}
a
,
c
,
{
1
}
b
)
,
(\{1\}^a,c,\{1\}^b),
(
{
2
}
a
,
c
,
{
2
}
b
)
(\{2\}^a,c,\{2\}^b)
and prove a number of congruences for these sums modulo a prime
p
.
p.
The congruences obtained allow us to find nice
p
p
-analogues of Leshchiner’s series for zeta values and to refine a result due to M. Hoffman and J. Zhao about the set of generators of the multiple harmonic sums of weight
7
7
and
9
9
modulo
p
p
. As a further application we provide a new proof of Zagier’s formula for
ζ
∗
(
{
2
}
a
,
3
,
{
2
}
b
)
\zeta ^{*}(\{2\}^a,3,\{2\}^b)
based on a finite identity for partial sums of the zeta-star series.