A193601 Augmentation of the triangle A062344. See Comments.

1, 1, 2, 1, 6, 10, 1, 12, 49, 76, 1, 20, 149, 508, 756, 1, 30, 354, 2082, 6353, 9192, 1, 42, 720, 6484, 32852, 92750, 131406, 1, 56, 1315, 16820, 127365, 580606, 1545757, 2153912, 1, 72, 2219, 38256, 404559, 2706150, 11385058, 28931758, 39768798

Offset: 0

Author

Clark Kimberling, Jul 31 2011

Keywords

• nonn
• tabl

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

Examples

			First 5 rows of A193601:
1
1...2
1...6....10
1...12...49...76
1...20...149..508...756
		

Crossrefs

Cf. A193091, A062344.

Programs

Mathematica

p[n_, k_] := Binomial[2 n, k] (* A062344 *)
Table[p[n, k], {n, 0, 5}, {k, 0, n}]
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}]] (* A193601 *)
Flatten[Table[v[n], {n, 0, 8}]]