A101751 - cp's OEIS frontend

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=[2n+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)!.

%I A101751 #6 Jun 16 2016 23:27:26
%S A101751 1,0,1,3,-6,32,264,-2024,2400,3420,55800,-666540,909720,2570400,90440,
%T A101751 13101144,72406040,-3757930680,13117344800,72965762016,-261763004160
%N 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)!.
%e A101751 Fact(8) = 5040; substituting n=8 in the formula of the k-th row we obtain k=4 and the coefficients
%e A101751 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.
%Y A101751 Cf. A008276, A094216, A000142, A094638, A101752, A003422, A101559, A101032, A099731.
%K A101751 sign,tabl
%O A101751 1,4
%A A101751 _André F. Labossière_, Dec 17 2004

cp's OEIS Frontend

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)!.

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=[2n+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)!.