Odd triangle n!. This table read by rows gives the coefficients of sum formulas of n-th Factorials (A000142). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+3+(-1)^n]/4 and T(i,k) satisfies n! = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!.
A102410
Odd triangle n!. This table read by rows gives the coefficients of sum formulas of n-th Factorials (A000142). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+3+(-1)^n]/4 and T(i,k) satisfies n! = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!.
Terms
- a(0) =1a(1) =0a(2) =0a(3) =-6a(4) =3a(5) =1a(6) =0a(7) =2400a(8) =-2024a(9) =264a(10) =32a(11) =0a(12) =2570400a(13) =909720a(14) =-666540a(15) =55800a(16) =3420a(17) =0a(18) =-19071521280a(19) =12195884736a(20) =-762499920a(21) =-282106440a(22) =22425480a(23) =741384a(24) =840a(29) =-125442525600a(30) =14164990560a(31) =280576800
External references
- oeis: A102410