Which scripture says that a sannyāsi can liberate 21 generations of ancestors without performing the śrāddha?

Question

As most people know when a Hindu takes up sannyāsa, he no longer performs the daily and other rituals like the śrāddha that normal householders do.

Swami Chandrasekarendra Saraswati in the book Hindu Dharma: The Universal Way of Life ^§ explains as below.

The Brahmin is born with three debts: he owes a debts to the sages, to the celestials and to the fathers. He repays the first by learning the Vedas as a student-bachelor; the second by taking a wife and performing sacrifices; and the third by begetting a son. So without marriage he cannot repay the second and third debts.

Sons are primarily intended for the repayment of the debts to the fathers. Performing the sraddha ceremony is not enough. Forefathers of the past three generations are to be made to ascend from the manes. So even after a man dies, for two generations the daily libations must be offered to him. That is why the birth of a son is considered important. (The case of the naisthika brahmacarin and the sannyasin is different. Because of their inner purity and enlightenment, they can liberate, not just two generations, but twenty-one generations of fathers without performing any sraddha ceremony).

[Hindu Dharma » Grhasthasrama » Grhastha and Grhini]

I'm specifically interested in the line marked in bold above.

Which Hindu scripture says that (naiṣṭhika) brahmacārīs and sannyāsīs can liberate souls of deceased parents and 21 generations of their ancestors without performing the śrāddha?

^§ _{An older and copyright-free version of this book is available for free here.}

Answer 1

The book Dharma Bindu(Essence of all Dharma Shastras) quotes Daksha Prajapati,in the context of discussing "Sannyasa Dharma":

Dakshan Prajapati affirms:

Trimshatparaamstrim shadaparaan trimshacchhapara –tah paraan, Sadyassannyasanaa deva narakaattraayete pitraan.

On account of Sanyasa of a person in a vamsha, Pitru Devatas of thirty generations before and another thirty generations ahead would be saved from narakas!

So,first of all it talks about 30 generations and not 21 and secondly i'm not sure which scripture is the source of that verse.It is natural to look in the Daksha Smriti first and i did too but apparently it does not contain the verse.

Will try to update on the source soon.

Update

The Sannyasopanishad(Chapter 2,Verse 10) (related to Samaveda) talks about 60 generations:

9. Seeing a Brahmana who has renounced the world t he sun moves from his place (thinking), ‘This person will reach Brahman breaking through my disc’.

10. That wise man who says ‘I have renounced’ raises to glory sixty generations of his family before him and sixty generations after him.