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A220399
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A convolution triangle of numbers obtained from A057682.
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1
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1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 3, 10, 6, 1, 0, 0, 18, 21, 8, 1, 0, -9, 21, 53, 36, 10, 1, 0, -27, 0, 99, 116, 55, 12, 1, 0, -54, -81, 117, 286, 215, 78, 14, 1, 0, -81, -270, -27, 528, 650, 358, 105, 16, 1
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OFFSET
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0,5
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COMMENTS
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Triangle T(n,k) given by (0, 2, -1/2, 3/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
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LINKS
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FORMULA
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G.f.: (1-3*x+3*x^2)/(1-3*x-3*x*y+3*x^2+x^2*y)
G.f for k-th column: ((x-x^2)/(1-3*x+3*x^2))^k.
T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - 3*T(n-2,k) - T(n-2,k-1), T(0,0) = 1, T(1,0) = T(2,0) = 0, T(n,k) = 0 if k<0 or if k>n.
Sum_{k, 0<=k<=n, n>0} T(n,k) = A001792(n-1).
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EXAMPLE
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Triangle begins :
1
0, 1
0, 2, 1
0, 3, 4, 1
0, 3, 10, 6, 1
0, 0, 18, 21, 8, 1
0, -9, 21, 53, 36, 10, 1
0, -27, 0, 99, 116, 55, 12, 1
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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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