{{1, 1, 1/2, 1/6, 1/24, 1/120},{0, q, q, 1+1/2q, 1+1/6q, 1/2+1/24q},{0, 0, 1, 1, 1/2, 1/6},{1, 0, 0, 0, 0, 0},{1, -1, 1/2, -1/6, 1/24, -1/120},{1,-2,2,-4/3,2/3, -4/15}}^(-1){{a},{b},{c},{d},{e},{f}}

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