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A291207
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Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of continued fraction 1/(1 + x/(1 - 2^k*x/(1 + 3^k*x/(1 - 4^k*x/(1 + 5^k*x/(1 - ...)))))).
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1
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1, 1, -1, 1, -1, 0, 1, -1, -1, 1, 1, -1, -3, 5, 0, 1, -1, -7, 27, 17, -2, 1, -1, -15, 167, 441, -121, 0, 1, -1, -31, 1071, 10673, -11529, -721, 5, 1, -1, -63, 6815, 262305, -1337713, -442827, 6845, 0, 1, -1, -127, 42687, 6525377, -161721441, -297209047, 23444883, 58337, -14
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OFFSET
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0,13
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LINKS
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FORMULA
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G.f. of column k: 1/(1 + x/(1 - 2^k*x/(1 + 3^k*x/(1 - 4^k*x/(1 + 5^k*x/(1 - ...)))))), a continued fraction.
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EXAMPLE
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G.f. of column k: A_k(x) = 1 - x + (1 - 2^k)*x^2 + (2^(k + 1) - 4^k + 6^k - 1)*x^3 + ...
Square array begins:
1, 1, 1, 1, 1, 1, ...
-1, -1, -1, -1, -1, -1, ...
0, -1, -3, -7, -15, -31, ...
1, 5, 27, 167, 1071, 6815, ...
0, 17, 441, 10673, 262305, 6525377, ...
-2, -121, -11529, -1337713, -161721441, -19802585281, ...
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MATHEMATICA
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Table[Function[k, SeriesCoefficient[1/(1 + ContinuedFractionK[-(-1)^i i^k x, 1, {i, 1, n}]), {x, 0, n}]][j - n], {j, 0, 9}, {n, 0, j}] // Flatten
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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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