theorem_check
Theorem check of the node's own rule. All operations
Parameters (4)
- all
- liu_wang 183 proof steps, 183 sequences
- three_term_recurrence 128 proof steps, 62 sequences
- liu_wang_derivative_lag 39 proof steps, 39 sequences
- ma_wang_interval 20 proof steps, 20 sequences
304 sequences
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A069466: Triangle T(n, k) of numbers of square lattice walks that start and end at origin after 2*n steps and contain exactly k steps to the east, possibly touching origin at intermediate stages.
1 · 2, 2 · 6, 24, 6 · 20, 180, 180, 20 … row sums 1, 4, 36, 400, 4900, 63504, 853776, …
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A027467: Triangle whose (n,k)-th entry is 15^(n-k)*binomial(n,k).
1 · 15, 1 · 225, 30, 1 · 3375, 675, 45, 1 … row sums 1, 16, 256, 4096, 65536, 1048576, …
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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, …
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A327997: Triangle read by rows: coefficients of the polynomials given by KummerU(-n, 1 - n - x, 3).
1 · 3, 1 · 9, 7, 1 · 27, 38, 12, 1 … row sums 1, 4, 17, 78, 393, 2208, 13977, 100026, …