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%I #14 Feb 04 2023 09:48:43
%S 1,0,1,5,-16,8,69,-767,1314,117,1774,-30405,78914,69024
%N Table (read by rows) giving the coefficients of sum formulas of n-th Left factorials (A003422).
%C 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!.
%e !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.
%Y Cf. A094216.
%K sign,tabf,more,uned
%O 1,4
%A _André F. Labossière_, Dec 17 2004