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A193602
Augmentation of the triangle A122366. See Comments.
1
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.
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
Sequence in context: A221736 A077108 A075847 * A221125 A049967 A221780
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jul 31 2011
STATUS
approved