Diane has one 1-cent stamp, two identical 2-cent stamps, and so on, up to nine identical 9-cent stamps. In how many different arrangements can Diane paste exactly 10 cents worth of postage in a row across the top of an envelope? (Note, however, that simply rotating or inverting a stamp, or exchanging the positions of two stamps with the same denomination should be considered the same arrangement.)

Let's think step by step and output the final answer within \boxed{}.
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