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EXAMPLE
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1
0, 0, "0", 1
1, 0, "9", 0, 9, 0, 1
56, 216, "378", 435, 324, 189, 54", 27, 0, 1
13833, 49464, "84510", 90944, 69039, 38448, 16476, 5184, 1431, 216, 54, 0, 1
6699824, 23123880, "38358540", 40563765, 30573900, 17399178, 7723640, 2729295, 776520, 180100, 33372, 5355, 540, 90, 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 6 do seq(coeff(f(t, n, 3), t, m)/3!^n, m=0..3*n); od;
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