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A056939: Array read by antidiagonals: number of antichains (or order ideals) in the poset 3*m*n or plane partitions with rows <= m, columns <= n and entries <= 3.
A108838 → ⊙ C(n+1,k+1) (shift +1)
1 · 1, 1 · 1, 4, 1 · 1, 10, 10, 1 …
row sums 1, 2, 6, 22, 92, 422, 2074, 10754, …
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A154986: Triangle T(n, k) = coefficients of p(x, n) where p(x,n) = (x+1)*p(x, n-1) + n*(n-1)*x*p(x, n-2), read by rows.
1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 …
row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …
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A102547: Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal's triangle (A007318).
1 · 1 · 1 · 1, 1 …
row sums 1, 1, 1, 2, 3, 4, 6, 9, …
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A106246: Number triangle T(n,k)=C(n,k)C(2,n-k).
A023531 → (1/2)D²+2D+1
1 · 2, 1 · 1, 4, 1 · 0, 3, 6, 1 …
row sums 1, 3, 6, 10, 15, 21, 28, 36, …
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A039756: Triangle of B-analogs of Stirling numbers of 2nd kind.
1 · 1, 1 · 1, 4, 1 · 1, 9, 13, 1 …
row sums 1, 2, 6, 24, 116, 648, 4088, 28640, …
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A172431 → ⊙ C(n,k+1) (shift -1) → reverse
1 · 1, 1 · 1, 4, 1 · 1, 10, 9, 1 …
row sums 1, 2, 6, 21, 80, 322, 1347, 5798, …
(−∞, 0]
nonnegative
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A391045: Triangle read by rows: T(n,k) = binomial(n+1,k+1)*binomial(2*n-k+1,k)/(n+1), 0<=k<=n.
A172431 → ⊙ C(n,k+1) (shift -1)
1 · 1, 1 · 1, 4, 1 · 1, 9, 10, 1 …
row sums 1, 2, 6, 21, 80, 322, 1347, 5798, …
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A173018 → reverse (shift +1) → reverse
1 · 1 · 1, 1 · 1, 4, 1 …
row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
(−∞, 0]
nonnegative
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A023531 → (1/2)D²+2D+1 → reverse
1 · 1, 2 · 1, 4, 1 · 1, 6, 3 …
row sums 1, 3, 6, 10, 15, 21, 28, 36, …
(−∞, 0]
nonnegative
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A008459: Square the entries of Pascal's triangle.
1 · 1, 1 · 1, 4, 1 · 1, 9, 9, 1 …
row sums 1, 2, 6, 20, 70, 252, 924, 3432, …
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A272867: Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.
1 · 1, 4, 1 · 1, 8, 18, 8, 1 …
row sums 1, 6, 36, 216, 1296, 7776, 46656, …
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A039755: Triangle of B-analogs of Stirling numbers of the second kind.
1 · 1, 1 · 1, 4, 1 · 1, 13, 9, 1 …
row sums 1, 2, 6, 24, 116, 648, 4088, 28640, …
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A039756 → reverse
1 · 1, 1 · 1, 4, 1 · 1, 13, 9, 1 …
row sums 1, 2, 6, 24, 116, 648, 4088, 28640, …
(−∞, 0]
nonnegative
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A173018: Euler's triangle: triangle of Eulerian numbers T(n,k) (n>=0, 0 <= k <= n) read by rows.
1 · 1 · 1, 1 · 1, 4, 1 …
row sums 1, 1, 2, 6, 24, 120, 720, 5040, …
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A039755 → reverse
1 · 1, 1 · 1, 4, 1 · 1, 9, 13, 1 …
row sums 1, 2, 6, 24, 116, 648, 4088, 28640, …
(−∞, 0]
nonnegative
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A081577: Pascal-(1,2,1) array read by antidiagonals.
1 · 1, 1 · 1, 4, 1 · 1, 7, 7, 1 …
row sums 1, 2, 6, 16, 44, 120, 328, 896, …
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A008292: Eulerian
1 · 1, 1 · 1, 4, 1 · 1, 11, 11, 1 …
row sums 1, 2, 6, 24, 120, 720, 5040, 40320, …