(n, k, symbols)
return expand_mul(s)
r"""
        The second kind of Bell polynomials (incomplete Bell polynomials).

        Calculated by recurrence formula:

        .. math:: B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1}) =
                \sum_{m=1}^{n-k+1}
                \x_m \binom{n-1}{m-1} B_{n-m,k-1}(x_1, x_2, \dotsc, x_{n-m-k})

        where
            B_{0,0} = 1;
            B_{n,0} = 0; for n>=1
            B_{0,k} = 0; for k>=1
r"""
        The second kind of Bell polynomials (incomplete Bell polynomials).
r The second kind of Bell polynomials ( incomplete Bell polynomials ) .
def _bell_incomplete_poly(n, k, symbols):
        r"""
        The second kind of Bell polynomials (incomplete Bell polynomials).

        Calculated by recurrence formula:

        .. math:: B_{n,k}(x_1, x_2, \dotsc, x_{n-k+1}) =
                \sum_{m=1}^{n-k+1}
                \x_m \binom{n-1}{m-1} B_{n-m,k-1}(x_1, x_2, \dotsc, x_{n-m-k})

        where
            B_{0,0} = 1;
            B_{n,0} = 0; for n>=1
            B_{0,k} = 0; for k>=1

        """
        if (n == 0) and (k == 0):
            return S.One
        elif (n == 0) or (k == 0):
            return S.Zero
        s = S.Zero
        a = S.One
        for m in xrange(1, n - k + 2):
            s += a * bell._bell_incomplete_poly(
                n - m, k - 1, symbols) * symbols[m - 1]
            a = a * (n - m) / m
        return expand_mul(s)
def _bell_incomplete_poly ( n , k , symbols ) : if ( n == 0 ) and ( k == 0 ) : return S . One elif ( n == 0 ) or ( k == 0 ) : return S . Zero s = S . Zero a = S . One for m in xrange ( 1 , n - k + 2 ) : s += a * bell . _bell_incomplete_poly ( n - m , k - 1 , symbols ) * symbols [ m - 1 ] a = a * ( n - m ) / m return expand_mul ( s )