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A247507
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Square array read by ascending antidiagonals, n>=0, k>=0. Row n is the expansion of (1-n*x-sqrt(n^2*x^2-2*n*x-4*x+1))/(2*x).
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1
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1, 1, 1, 1, 2, 2, 1, 3, 6, 5, 1, 4, 12, 22, 14, 1, 5, 20, 57, 90, 42, 1, 6, 30, 116, 300, 394, 132, 1, 7, 42, 205, 740, 1686, 1806, 429, 1, 8, 56, 330, 1530, 5028, 9912, 8558, 1430, 1, 9, 72, 497, 2814, 12130, 35700, 60213, 41586, 4862
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OFFSET
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0,5
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LINKS
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FORMULA
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G.f. of row n: 1/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - ...))))), a continued fraction. - Ilya Gutkovskiy, Apr 06 2018
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EXAMPLE
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[0][1] [2] [3] [4] [5] [6] [7]
[0] 1, 1, 2, 5, 14, 42, 132, 429,.. A000108
[1] 1, 2, 6, 22, 90, 394, 1806, 8558,.. A006318
[2] 1, 3, 12, 57, 300, 1686, 9912, 60213,.. A047891
[3] 1, 4, 20, 116, 740, 5028, 35700, 261780,.. A082298
[4] 1, 5, 30, 205, 1530, 12130, 100380, 857405,.. A082301
[5] 1, 6, 42, 330, 2814, 25422, 239442, 2326434,.. A082302
[6] 1, 7, 56, 497, 4760, 48174, 507696, 5516133,.. A082305
[7] 1, 8, 72, 712, 7560, 84616, 985032, 11814728,.. A082366
[8] 1, 9, 90, 981, 11430, 140058, 1782900, 23369805,.. A082367
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MAPLE
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gf := n -> (1-n*x-sqrt(n^2*x^2-2*n*x-4*x+1))/(2*x):
for n from 0 to 10 do lprint(PolynomialTools:-CoefficientList( convert(series(gf(n), x, 8), polynom), x)) od;
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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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