Brackets Combination with the addition of

I have an interesting problem with the combination and I'm a little stuck

Allows you to define a function p (xn) that returns the number '()' for the equation x Now x can only be in the form x1 + x2 + x3 ... xn This function is defined for n> = 2

Examples:

P (x2) = (x1 + x2) = 1

p (x3) = ((x1 + x2) + x3) and (x1 + (x2 + x3))

p (x4) =

((x1 + x2) + (x3 + x4))

(((x1 + x2) + x3) + x4)

((x1 + (x2 + x3)) + x4)

(x1 + ((x2 + x3) + x4))

(x1 + (x2 + (x3 + x4)))

etc. The remark (x1 + (x2 + x3) + x4) is not a valid example for each +

there must be one ()

P, , , . , , ?

+5
1

, , - x 1 - x n. P (n).

n-1 node. k- . k , P (k). n-k , P (n-k) . , P (k) P (n-k) .

k 1 n-1, , n :

P(n) = P(1)P(n-1) + P(2)P(n-2) + ··· + P(n-2)P(2) + P(n-1)P(1)

@DSM , . , . . :

P(n) = C(2n,n)/(n+1)                where C(n,k) = n! / (k!(n-k)!)
+2

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