Common tiger lily, Lilium lancifolium (Lilium tigrinum). Those formations are known as 'bulbils' and are aerial bulblets, not seeds. They can be removed carefully later in summer (after flowering and before the leaves dry) and planted in good potting soil about 1/2" deep. Overwinter them in this manner and then separate and pot up the larger bulbs next spring. It should take about 2-3 years before they reach blooming size.
Propagation of tiger lilies by bulbils