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A127068
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Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(3,n).
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1
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1, 3, 4, -30, -216, 420, 14400, 22680, -1411200, -8482320, 195955200, 2399997600, -36883123200, -788107320000, 9066542284800, 318173519664000, -2824576634880000, -159078423407904000, 1088403529973760000, 97970873094110016000, -508476519708917760000, -73631427647097640320000
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