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=[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)!.
Terms
- a(0) =1a(1) =0a(2) =1a(3) =3a(4) =-6a(5) =32a(6) =264a(7) =-2024a(8) =2400a(9) =3420a(10) =55800a(11) =-666540a(12) =909720a(13) =2570400a(14) =90440a(15) =13101144a(16) =72406040a(17) =-3757930680a(18) =13117344800a(19) =72965762016a(20) =-261763004160
External references
- oeis: A101751