A132466 Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(8,n).
0, 0, 0, 0, 0, 0, 0, 1, 80, 1944, 25200, 217800, 1411344, 7361640, 32391216, 124227675, 425339200, 1323786464, 3797876160, 10155802176, 25539739200, 60844672800, 138154965696, 300509773245, 628886888784, 1270898695000, 2488029830000, 4731583685400, 8762192010000
Offset: 1
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See A132458 for further information.