A101752 Table (read by rows) giving the coefficients of sum formulas of n-th Left factorials (A003422).

1, 0, 1, 5, -16, 8, 69, -767, 1314, 117, 1774, -30405, 78914, 69024

Offset: 1

Author

André F. Labossière, Dec 17 2004

Keywords

• sign
• tabf
• more
• uned

Comments

The k-th row (k>=1) contains T(i,k) for i=1 to k+1, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies !n = Sum_{i=1..k+1} T(i,k) * n^(k-i+1) / k!.

Examples

			!7 = 874; substituting n=7 in the formula of the k-th row we obtain k=4 and the coefficients T(i,4) will be the following: 117,1774,-30405,78914,69024, => !7 = [ 117*7^4 +1774*7^3 -30405*7^2 +78914*7 +69024 ]/4! = 874.
		

Crossrefs

Cf. A094216.