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MATHEMATICA
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Morse[a_, b_] := Module[{i, j, k, m, x, y, A}, A[0, 0]=1; m = a+b; For[k=1, k <= m, k++, For[y=0, y <= b, y++, x = k-y; If[y==0, A[x, y] = 1/(2^x), If[x>0, A[x, y] = (1/(x+2y+1))((x+1)A[x+1, y-1] + 1/2 (x+1)A[x-1, y] + 1/2 (x+1)Sum[Sum[A[i, j]A[x-i, y-1-j], {j, 0, y-1}], {i, 0, x}]), A[x, y] = (1/(2y+1))((x+1)A[x+1, y-1] + 1/2 (x+1)Sum[Sum[A[i, j]A[x-i, y-1-j], {j, 0, y-1}], {i, 0, x}])]]]]; a! (2b+1)! A[a, b]];
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