Triangle read by rows: let t1(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; then T(n,m)=2*t1(n + 1, k) - (m! - n! + (-m + n)!).

A155452

Triangle read by rows: let t1(n,k)=Sum[(-1)^j Binomial[n + 1, j](k + 1 - j)^n, {j, 0, k + 1}]; then T(n,m)=2*t1(n + 1, k) - (m! - n! + (-m + n)!).

Terms

    a(0) =1a(1) =1a(2) =1a(3) =1a(4) =8a(5) =1a(6) =1a(7) =25a(8) =25a(9) =1a(10) =1a(11) =69a(12) =152a(13) =69a(14) =1a(15) =1a(16) =209a(17) =716a(18) =716a(19) =209a(20) =1a(21) =1a(22) =839a(23) =3076a(24) =5540a(25) =3076a(26) =839a(27) =1a(28) =1a(29) =4813

External references