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EXAMPLE
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"1"
"0", 0, 0, 0, 0, 1
'1", 0, 25, 0, 100, 0, 100, 0, 25, 0, 1
"2252", 15150, 48600, 99350, 144150, 156753, 131000, 87075, 45000,
19300, 6000, 1800, 250, 75, 0, 1
"44127009", 274314600, 822998550, 1583402400, 2189652825, 2311947008,
1932997200, 1310330400, 731686550, 340071600, 132480756,
43364000, 11973150, 2760000, 541600, 84000, 12225, 1000, 150, 0, 1
etc...
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MAPLE
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p := (x, k)->k!^2*sum(x^j/((k-j)!^2*j!), j=0..k); R := (x, n, k)->p(x, k)^n; f := (t, n, k)->sum(coeff(R(x, n, k), x, j)*(t-1)^j*(n*k-j)!, j=0..n*k); for n from 0 to 8 do seq(coeff(f(t, n, 5), t, m)/5!^n, m=0..5*n); od;
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