Is there any notation to input falling or rising factorials on WolframAlpha?, the site has info about but i cant find nothing more.
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As one comment and one answer point out, the rising factorial can be expressed in terms of Mathematica's PochammerSymbol and the falling factorial in terms of FactorialPower so it's not surprising that these inputs work in WolframAlpha. You can use the terms "rising factorial" and "falling factorial as well, though. Here are a few examples.
One input that does not currently work (and perhaps why you missed this) is "falling factorial x,n". I'd not be surprised to see that working soon, though.