The payments you made to the departing partner and the note payable to the partner are to purchase the partner's interest in the business. These are not income or deductions for the business, so it doesn't impact the partnership tax return.
For you, the payment/note payable represent an increase in your basis for the business you still own. These loans are actually loans to you to buy the other partner's interest in the business, not loans to the business itself. They do not show up on your personal tax return.
For the departing partner, those same payments/note payable represent proceeds from the sale of his interest in the business. Depending on the departing partner's basis in their portion of the business, they will have a gain on loss on the sale of a business. That gain or loss is reported on the departing partner's personal income tax return.
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