A101751 Table (read by rows) giving the coefficients of sum formulas of n-th Factorials (A000142). The k-th row (k>=1, n>=2) contains T(i,k) for i=1 to k+1, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies Fact(n) = Sum_{i=1..k+1} T(i,k) * (n-1)^(k-i+1) / (2*k-2)!.

1, 0, 1, 3, -6, 32, 264, -2024, 2400, 3420, 55800, -666540, 909720, 2570400, 90440, 13101144, 72406040, -3757930680, 13117344800, 72965762016, -261763004160

Offset: 1

Author

André F. Labossière, Dec 17 2004

Keywords

• sign
• tabl

Examples

			Fact(8) = 5040; substituting n=8 in the formula of the k-th row we obtain k=4 and the coefficients
T(i,4) will be the following: 3420,55800,-666540,909720,2570400, => Fact(8) = [ 3420*7^4 +55800*7^3 -666540*7^2 +909720*7 +2570400 ]/6! = 7! =5040.
		

Crossrefs

Cf. A008276, A094216, A000142, A094638, A101752, A003422, A101559, A101032, A099731.