A193593 Augmentation of the triangle A193592. See Comments.
1, 1, 1, 1, 3, 2, 1, 6, 10, 6, 1, 10, 31, 40, 23, 1, 15, 75, 166, 187, 105, 1, 21, 155, 530, 958, 993, 549, 1, 28, 287, 1415, 3786, 5988, 5865, 3207, 1, 36, 490, 3311, 12441, 28056, 40380, 37947, 20577, 1, 45, 786, 7000, 35469, 109451, 217720, 292092
Offset: 0
Examples
First 5 rows: 1 1...1 1...3...2 1...6...10...6 1...10..31...40...23 Rows reversed as in Callan's n-edge increasing ordered trees with outdegree k: 1 0 1 0 1 1 0 2 3 1 0 6 10 6 1 0 23 40 31 10 1 0 105 187 166 75 15 1 0 549 993 958 530 155 21 1 0 3207 5865 5988 3786 1415 287 28 1 0 20577 37947 40380 28056 12441 3311 490 36 1 0 143239 265901 292092 217720 109451 35469 7000 786 45 1
Links
- D. Callan, A bijection to count (1-23-4)-avoiding permutations, arXiv:1008.2375 (rows reversed)
Programs
-
Mathematica
p[n_, 0] := 1; p[n_, k_] := n + 1 - k /; k > 0; Table[p[n, k], {n, 0, 5}, {k, 0, n}] (* A193592 *) m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}] TableForm[m[4]] w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1]; v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]}; v[n_] := v[n - 1].m[n] TableForm[Table[v[n], {n, 0, 12}]] (* A193593 *) Flatten[Table[v[n], {n, 0, 10}]]
Comments