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Explicit formulas for computation of the Poincar\'e series for the algebrasof joint $SL_2$-invariants and covariants of $n$ linear forms in terms ofNarayana polynomials are found. Also, for these algebras we calculate thedegrees and asymptotic behavious of the degrees.

The Poincar\'e series for the algebras of joint invariants and covariants of $n$ linear forms