Triangle read by rows: first define the Narayana numbers: Y(n,m)=Binomial[n, m]*Binomial[n + 1, m + 1]/(n - m + 1); then t(n,m)=Sum[(-1)^j *Y(n + 1, j)*(k + 1 - j)^n, {j, 0, k + 1}].
A155796
Triangle read by rows: first define the Narayana numbers: Y(n,m)=Binomial[n, m]*Binomial[n + 1, m + 1]/(n - m + 1); then t(n,m)=Sum[(-1)^j *Y(n + 1, j)*(k + 1 - j)^n, {j, 0, k + 1}].
Terms
- a(0) =1a(1) =1a(2) =-2a(3) =1a(4) =-2a(5) =-33a(6) =1a(7) =1a(8) =-109a(9) =-209a(10) =1a(11) =11a(12) =-324a(13) =-894a(14) =1641a(15) =1a(16) =36a(17) =-867a(18) =-4262a(19) =12951a(20) =85926a(21) =1a(22) =92a(23) =-2085a(24) =-20516a(25) =74369a(26) =625164a(27) =1435939a(28) =1a(29) =211
External references
- oeis: A155796