A193602 Augmentation of the triangle A122366. See Comments.

1, 1, 3, 1, 8, 19, 1, 15, 80, 172, 1, 24, 221, 971, 1967, 1, 35, 492, 3547, 13809, 26832, 1, 48, 955, 10186, 62840, 224529, 422609, 1, 63, 1684, 24890, 222132, 1226003, 4102449, 7525966, 1, 80, 2765, 54077, 658319, 5167948, 26193697, 83159133

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..43.

Example

First five rows of A193602:
1
1...3
1...8....19
1...15...80...172
1...24...221..971...1967

Mathematica

p[n_, k_] := Binomial[2 n + 1, k] (* A122366 *)
Table[p[n, k], {n, 0, 7}, {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}]] (* A193602 *)
Flatten[Table[v[n], {n, 0, 8}]]

Crossrefs

Cf. A122366, A193091.

Sequence in context: A221736 A077108 A075847 * A221125 A049967 A221780

Adjacent sequences: A193599 A193600 A193601 * A193603 A193604 A193605

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 31 2011

Status

approved