Triangle read by rows: T[n, m] = Sum[m^3 - 3*m^2*k + 3*m*k^2 - k^3, {k, 0, n - 1}] + m^4.

Terms

a(0) =1a(1) =0a(2) =2a(3) =-1a(4) =2a(5) =25a(6) =-9a(7) =1a(8) =25a(9) =117a(10) =-36a(11) =-7a(12) =24a(13) =117a(14) =356a(15) =-100a(16) =-34a(17) =16a(18) =116a(19) =356a(20) =850a(21) =-225a(22) =-98a(23) =-11a(24) =108a(25) =355a(26) =850a(27) =1737a(28) =-441a(29) =-223