Catalan numbers: Difference between revisions
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15 = 9694845
</pre>
=={{header|AutoHotkey}}==
As AutoHotkey has no BigInt, the formula had to be tweaked to prevent overflow. It still fails after n=22
<lang AHK>Loop 15
out .= "`n" Catalan(A_Index)
Msgbox % clipboard := SubStr(out, 2)
catalan( n ) {
; By [VxE]. Returns ((2n)! / ((n + 1)! * n!)) if 0 <= N <= 22 (higher than 22 results in overflow)
If ( n < 3 ) ; values less than 3 are handled specially
Return n < 0 ? "" : n = 0 ? 1 : n
i := 1 ; initialize the accumulator to 1
Loop % n - 1 >> 1 ; build the numerator by multiplying odd values between 2N and N+1
i *= 1 + ( n - A_Index << 1 )
i <<= ( n - 2 >> 1 ) ; multiply the numerator by powers of 2 according to N
Loop % n - 3 >> 1 ; finish up by (integer) dividing by each of the non-cancelling factors
i //= A_Index + 2
Return i
}</lang>
Output:
<pre>1
2
5
14
42
132
429
1430
4862
16796
58786
208012
742900
2674440
9694845</pre>
=={{header|BASIC}}==
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