Combinatorial Analysis - 26.5 Lattice Paths: Catalan Numbers
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 26.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{n+1}\binom{2n}{n} = \frac{1}{2n+1}\binom{2n+1}{n}}
\frac{1}{n+1}\binom{2n}{n} = \frac{1}{2n+1}\binom{2n+1}{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(n + 1)*binomial(2*n,n) = (1)/(2*n + 1)*binomial(2*n + 1,n)
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Divide[1,n + 1]*Binomial[2*n,n] == Divide[1,2*n + 1]*Binomial[2*n + 1,n]
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Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 26.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2n+1}\binom{2n+1}{n} = \binom{2n}{n}-\binom{2n}{n-1}}
\frac{1}{2n+1}\binom{2n+1}{n} = \binom{2n}{n}-\binom{2n}{n-1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (1)/(2*n + 1)*binomial(2*n + 1,n) = binomial(2*n,n)-binomial(2*n,n - 1)
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Divide[1,2*n + 1]*Binomial[2*n + 1,n] == Binomial[2*n,n]-Binomial[2*n,n - 1]
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Successful | Failure | Skip - symbolical successful subtest | Successful [Tested: 3] |
| 26.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{2n}{n}-\binom{2n}{n-1} = \binom{2n-1}{n}-\binom{2n-1}{n+1}}
\binom{2n}{n}-\binom{2n}{n-1} = \binom{2n-1}{n}-\binom{2n-1}{n+1} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | binomial(2*n,n)-binomial(2*n,n - 1) = binomial(2*n - 1,n)-binomial(2*n - 1,n + 1)
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Binomial[2*n,n]-Binomial[2*n,n - 1] == Binomial[2*n - 1,n]-Binomial[2*n - 1,n + 1]
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |