Unlike the numbers that precede 20, the palm is oriented outward in all the numbers after 20. For these larger numbers, number signs that include 1-5 do not face inward as they do in the number signs for 1-20. There is one exception here: for the sign TWENTY-ONE, one variant sign has the palm oriented inward.
Note that in the number signs 21-29, the combining form for 20 does not have contact between the thumb and first finger, as the independent sign TWENTY does. Instead, the twenties "decade" is signified by an L-handshape oriented outward. Where did this L-handshape come from? One possibility is that the source for this combining-form for "twenty" lies in the sign DEUX 'two' in French Sign Language. Remember that there is a strong historical relationship between ASL and French Sign Language.
If you speak English at the same time that you sign, you may erroneously tend to produce numbers that would consist of the sign TWENTY followed, say, by the number sign THREE. This is incorrect; for this reason try not to speak or mouth in English when you produce these number signs. None of the number signs TWENTY-ONE through TWENTY-NINE consists of a sequence of two signs beginning with the independent sign TWENTY followed by a sign for a digit.