def _itgs_iterator(self, base_ring):
r"""
The isomorphism type generating series is given by
`\frac{1}{1-x}`.
EXAMPLES::
sage: P = species.PartitionSpecies()
sage: g = P.isotype_generating_series()
sage: g.coefficients(10)
[1, 1, 2, 3, 5, 7, 11, 15, 22, 30]
"""
from sage.combinat.partitions import number_of_partitions
for n in _integers_from(0):
yield self._weight*base_ring(number_of_partitions(n))
def _itgs_iterator(self, base_ring):
r"""
The isomorphism type generating series is given by
`\frac{1}{1-x}`.
EXAMPLES::
sage: P = species.PermutationSpecies()
sage: g = P.isotype_generating_series()
sage: g.coefficients(10)
[1, 1, 2, 3, 5, 7, 11, 15, 22, 30]
"""
from sage.combinat.partitions import number_of_partitions
for n in _integers_from(0):
yield base_ring(number_of_partitions(n))