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A193607
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Augmentation of the triangle A011973. See Comments.
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2
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1, 1, 1, 1, 4, 2, 1, 9, 20, 7, 1, 16, 80, 131, 37, 1, 25, 220, 806, 1085, 265, 1, 36, 490, 3130, 9360, 10952, 2402, 1, 49, 952, 9325, 48224, 124498, 130852, 26371, 1, 64, 1680, 23317, 183569, 813886, 1876101, 1809430, 340272
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OFFSET
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0,5
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COMMENTS
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For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
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LINKS
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EXAMPLE
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1
1...1
1...4....2
1...9....20...7
1...16...80...131...37
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MATHEMATICA
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p[n_, k_] := Binomial[2 n - k, k];
Table[p[n, k], {n, 0, 7}, {k, 0, n}] (* A011973 *)
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, 9}]] (* A193607 *)
Flatten[Table[v[n], {n, 0, 8}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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