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A144218
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Equals product A*B, where A is an infinite lower triangular matrix with A086246 in every column and B is the diagonal matrix with A001006 as diagonal.
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1
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1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 4, 2, 2, 4, 9, 9, 4, 4, 4, 9, 21, 21, 9, 8, 8, 9, 21, 51, 51, 21, 18, 16, 18, 21, 51, 127, 127, 51, 42, 36, 36, 42, 51, 127, 323, 323, 127, 102, 84, 81, 84, 102, 127, 323, 835, 835, 323, 254, 204, 189, 189, 204, 254, 323, 835, 2188
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OFFSET
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0,6
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COMMENTS
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Row sums give A001006 without the initial 1.
Sum of n-th row terms = rightmost term of next row.
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
1, 1, 2;
2, 1, 2, 4;
4, 2, 2, 4, 9;
9, 4, 4, 4, 9, 21;
21, 9, 8, 8, 9, 21, 51;
51, 21, 18, 16, 18, 21, 51, 127;
127, 51, 42, 36, 36, 42, 51, 127, 323;
323, 127, 102, 84, 81, 84, 102, 127, 323, 835;
835, 323, 254, 204, 189, 189, 204, 254, 323, 835, 2188;
...
Row 4 = (4, 2, 2, 4, 9) = termwise products of (4, 2, 1, 1, 1) and (1, 1, 2, 4, 9) = (4*1, 2*1, 1*2, 1*4, 1*9).
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MATHEMATICA
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nmax = 10;
T[0, 0] = T[1, 0] = 1;
T[n_, 0] := Hypergeometric2F1[3/2, 1-n, 3, 4] // Abs;
T[n_, n_] := Hypergeometric2F1[(1-n)/2, -n/2, 2, 4];
row[n_] := row[n] = Table[T[m, 0], {m, n, 0, -1}]*Table[T[m, m], {m, 0, n} ];
T[n_, k_] /; 0<k<n := row[n][[k+1]];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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