A132465 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(7,n).
0, 0, 0, 0, 0, 0, 1, 63, 1232, 13104, 94500, 518364, 2317392, 8833968, 29630601, 89464375, 247351104, 634542272, 1526183568, 3470399856, 7511688000, 15564217536, 31016698713, 59686024167, 111284511184, 201628350000, 355896440900, 613353440700, 1034083486800
Offset: 1
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See A132458 for further information.