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@VladimirReshetnikov
Created November 7, 2016 05:43
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ClearAll[p, n];
p[1] = 1;
p[n_] := p[n] = Expand[FunctionExpand[Sum[Binomial[n-1, k-1] QBinomial[n-2, k-1, q] p[k] p[n-k] q^(n-k-1), {k, 1, n-1}]]];
For[n = 1, True, n++, Print[p[n]]]
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