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A193601 Augmentation of the triangle A062344. See Comments. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
LINKS
EXAMPLE
First 5 rows of A193601:
1
1...2
1...6....10
1...12...49...76
1...20...149..508...756
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}]]
CROSSREFS
Sequence in context: A025252 A348108 A177863 * A157402 A069114 A173773
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jul 31 2011
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)