Even triangle !n. This table read by rows gives the coefficients of sum formulas of n-th Left factorials (A003422). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies !n = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!.
A102411
Even triangle !n. This table read by rows gives the coefficients of sum formulas of n-th Left factorials (A003422). The k-th row (6>=k>=1) contains T(i,k) for i=1 to k+2, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies !n = Sum_{i=1..k+2} T(i,k) * n^(i-1) / (2*k-2)!.
Terms
- a(0) =0a(1) =1a(2) =0a(3) =-16a(4) =5a(5) =1a(6) =0a(7) =5256a(8) =-3068a(9) =276a(10) =32a(11) =0a(12) =2070720a(13) =2367420a(14) =-912150a(15) =53220a(16) =3510a(17) =0a(18) =-36031524480a(19) =15327895296a(20) =-40587120a(21) =-387492840a(22) =21414120a(23) =758184a(24) =840a(29) =-195611371200a(30) =13639812480a(31) =285616800a(32) =453600
External references
- oeis: A102411