A193630 Augmentation of the triangle A074909. See Comments.
1, 1, 2, 1, 5, 7, 1, 9, 28, 33, 1, 14, 74, 181, 191, 1, 20, 159, 637, 1333, 1297, 1, 27, 300, 1767, 5906, 11029, 10063, 1, 35, 517, 4190, 20256, 59324, 101351, 87669, 1, 44, 833, 8873, 58339, 244125, 645146, 1024949, 847015, 1, 54, 1274, 17241, 147680
Offset: 0
Examples
First five rows of A193607: 1 1...2 1...5....7 1...9....28...33 1...14...74...181...191
Programs
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Mathematica
p[n_, k_] := Binomial[n + 1, k]; Table[p[n, k], {n, 0, 7}, {k, 0, n}] (* A074909 *) 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, 6}]] (* A193630 *) Flatten[Table[v[n], {n, 0, 8}]]
Comments