Even 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+3, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies n! = Sum_{i=1..k+3} T(i,k) * n^(i-1) / (2*k-2)!.
A102409
Even 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+3, where k=[2*n+1+(-1)^(n-1)]/4 and T(i,k) satisfies n! = Sum_{i=1..k+3} T(i,k) * n^(i-1) / (2*k-2)!.
Terms
- a(0) =0a(1) =1a(2) =0a(3) =0a(4) =0a(5) =-20a(6) =8a(7) =0a(8) =0a(9) =20280a(10) =-6530a(11) =-1275a(12) =362a(13) =3a(14) =0a(15) =-8749440a(16) =21627600a(17) =-4871940a(18) =-66510a(19) =48300a(20) =390a(21) =0a(22) =-261763004160a(23) =72965762016a(24) =13117344800a(25) =-3757930680a(26) =72406040a(27) =13101144a(28) =90440a(29) =0
External references
- oeis: A102409