Triangle of numbers a(n,k), n>=3, ceiling((n-3)/2)<=k<=n-3: a(n,k)=Sum[ Binomial[x + y + z, x]*Binomial[y + z, y]*Binomial[n - 2 - x - 2*y - 2*z, 2*n - 2*y - 5 - 2*k]*(2^x)*((-1)^z), {z, 0, (2*k - n + 3)/2}, {y, 0, n - 3 - k}, {x, 0, 2*k - n + 3 - 2*z}].
A128781
Triangle of numbers a(n,k), n>=3, ceiling((n-3)/2)<=k<=n-3: a(n,k)=Sum[ Binomial[x + y + z, x]*Binomial[y + z, y]*Binomial[n - 2 - x - 2*y - 2*z, 2*n - 2*y - 5 - 2*k]*(2^x)*((-1)^z), {z, 0, (2*k - n + 3)/2}, {y, 0, n - 3 - k}, {x, 0, 2*k - n + 3 - 2*z}].
Terms
- a(0) =1a(1) =4a(2) =2a(3) =10a(4) =12a(5) =20a(6) =3a(7) =42a(8) =35a(9) =24a(10) =112a(11) =56a(12) =4a(13) =108a(14) =252a(15) =84a(16) =40a(17) =360a(18) =504a(19) =120a(20) =5a(21) =220a(22) =990a(23) =924a(24) =165a(25) =60a(26) =880a(27) =2376a(28) =1584a(29) =220
External references
- oeis: A128781