Hemorrhagic Disease of the Newborn (HDN): This condition is caused by vitamin K deficiency, which can lead to bleeding problems. The fact that the baby received vitamin K at delivery and still developed clots after feeding suggests that the condition might not be fully prevented or that there was a delay in its administration. However, this is the most direct condition related to the information provided.

Gastrointestinal Issues: Conditions such as gastroesophageal reflux or anatomic abnormalities could lead to bleeding after feeding, presenting as clots.
Infection or Sepsis: Infections can cause coagulopathy, leading to clotting issues. The timing after feeding might be coincidental.
Allergic Reaction to Formula: Though less common, an allergic reaction to formula could potentially cause gastrointestinal bleeding.

Disseminated Intravascular Coagulation (DIC): A serious disorder in which the proteins responsible for blood clotting become overactive, leading to the formation of small blood clots in various blood vessels throughout the body. This condition can be life-threatening and requires immediate attention.
Severe Congenital Coagulopathy: Conditions like factor XIII deficiency or other rare coagulation factor deficiencies could present with severe bleeding or clotting after minor trauma, such as the stress of feeding.

Congenital Thrombocytopenia: Rare conditions affecting platelet production or function could lead to clotting abnormalities.
Von Willebrand Disease: A genetic disorder caused by missing or defective von Willebrand factor (VWF), a clotting protein. It can lead to easy bruising, bleeding, and clotting issues, though it's less likely to present immediately after birth in such a dramatic fashion.
Other Congenital Bleeding Disorders: Such as afibrinogenemia or dysfibrinogenemia, which are extremely rare and would present with significant bleeding or clotting issues early in life.