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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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
EXAMPLE
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;
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));
CROSSREFS
Family: A009766 (Catalan's triangle, m=0), A001498 (m=1), A060058 (m=2), this triangle (m=3), A371997 (m=4).
Cf. A216966 (main diagonal).
Sequence in context: A178164 A216035 A171487 * A120704 A021506 A243264
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Apr 24 2024
STATUS
approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)