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A202328
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Triangle T(n,k) = coefficient of x^n in expansion of [x(1+x^2)/(1-x^2)]^k = sum(n>=k, T(n,k) x^n).
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0
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1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 2, 0, 6, 0, 1, 0, 8, 0, 8, 0, 1, 2, 0, 18, 0, 10, 0, 1, 0, 12, 0, 32, 0, 12, 0, 1, 2, 0, 38, 0, 50, 0, 14, 0, 1, 0, 16, 0, 88, 0, 72, 0, 16, 0, 1, 2, 0, 66, 0, 170, 0, 98, 0, 18, 0, 1, 0, 20, 0, 192, 0, 292, 0, 128, 0, 20, 0, 1, 2, 0, 102, 0, 450, 0, 462, 0, 162, 0, 22, 0, 1, 0, 24, 0, 360, 0, 912, 0, 688, 0, 200, 0, 24, 0, 1
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OFFSET
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1,4
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LINKS
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FORMULA
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T(n,k)=((sum(i=0..(n-k)/2, binomial(k,(n-k)/2-i)*binomial(k+i-1,k-1)))*((-1)^(n+k)+1))/2.
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EXAMPLE
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1
0, 1,
2, 0, 1,
0, 4, 0, 1,
2, 0, 6, 0, 1,
0, 8, 0, 8, 0, 1,
2, 0, 18, 0, 10, 0, 1
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PROG
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(Maxima)
T(n, k):=((sum(binomial(k, (n-k)/2-i)*binomial(k+i-1, k-1), i, 0, (n-k)/2))*((-1)^(n+k)+1))/2
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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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