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Yes, recursive is playable

...and is worth 17 points.

Found in the following dictionaries

Enable (Words with friends)
SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Recursive" Definition

adjective

Drawing upon itself, referring back.
Source: Wiktionary
Of a program or function that calls itself.
Source: Wiktionary
Of an expression, each term of which is determined by applying a formula to preceding terms.
Source: Wiktionary
Which can be computed by a theoretical model of a computer, in a finite amount of time.
Source: Wiktionary
Whose characteristic function is recursive (4).
Source: Wiktionary

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