A371996 Triangle read by rows: T(m, n, k) = 1 if k = 0 and T(m, n, k - 1) if k = n; otherwise (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) where m = 3.
1, 1, 1, 1, 9, 9, 1, 36, 297, 297, 1, 100, 2997, 24273, 24273, 1, 225, 17397, 493992, 3976209, 3976209, 1, 441, 72522, 5135400, 142632009, 1145032281, 1145032281, 1, 784, 241866, 35368650, 2406225609, 66113123724, 530050022073, 530050022073
Offset: 0
Examples
Triangle read by rows: [0] 1; [1] 1, 1; [2] 1, 9, 9; [3] 1, 36, 297, 297; [4] 1, 100, 2997, 24273, 24273; [5] 1, 225, 17397, 493992, 3976209, 3976209; [6] 1, 441, 72522, 5135400, 142632009, 1145032281, 1145032281;
Crossrefs
Programs
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Maple
T := proc(m, n, k) option remember; if k = 0 then 1 elif k = n then T(m, n, k-1) else (-1)^m*(k - n - 1)^m * T(m, n, k - 1) + T(m, n - 1, k) fi end: seq(seq(T(3, n, k), k = 0..n), n = 0..8));