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A086614
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Triangle read by rows, where T(n,k) is the coefficient of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x)^2 + xy*f(x,y)^2.
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2
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1, 2, 1, 3, 4, 2, 4, 10, 12, 5, 5, 20, 42, 40, 14, 6, 35, 112, 180, 140, 42, 7, 56, 252, 600, 770, 504, 132, 8, 84, 504, 1650, 3080, 3276, 1848, 429, 9, 120, 924, 3960, 10010, 15288, 13860, 6864, 1430, 10, 165, 1584, 8580, 28028, 57330, 73920, 58344, 25740
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n,k) = binomial(2*k, k-1)*binomial(n+k+1, n-k) / k for k > 0. # Peter Luschny, Jan 26 2018
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EXAMPLE
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Rows:
{1},
{2, 1},
{3, 4, 2},
{4, 10, 12, 5},
{5, 20, 42, 40, 14},
{6, 35, 112, 180, 140, 42},
{7, 56, 252, 600, 770, 504, 132},
{8, 84, 504, 1650, 3080, 3276, 1848, 429}, ...
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MAPLE
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T := (n, k) -> `if`(k=0, n+1, binomial(2*k, k-1)*binomial(n+k+1, n-k)/k):
for n from 0 to 8 do seq(T(n, k), k=0..n) od; # Peter Luschny, Jan 26 2018
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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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