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A198321
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Triangle T(n,k), read by rows, given by (0,1,0,0,0,0,0,0,0,0,0,...) DELTA (1,1,-1,1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
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1
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1, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 4, 6, 4, 0, 1, 5, 10, 10, 5, 0, 1, 6, 15, 20, 15, 6, 0, 1, 7, 21, 35, 35, 21, 7, 0, 1, 8, 28, 56, 70, 56, 28, 8, 0, 1, 9, 36, 84, 126, 126, 84, 36, 9, 0, 1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 0, 1, 11, 55, 165, 330
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OFFSET
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0,6
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COMMENTS
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LINKS
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FORMULA
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T(n,0)=0^n, T(n,k)=binomial(n,k-1) for 1<=k<=n.
Sum_{0<=k<=n} T(n,k)*x^k = x*((x+1)^n-x^n) for n>0.
G.f.: (1-(1+y)*x+y*(1+y)*x^2)/((1-(1+y)*x)*(1-y*x)).
T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k-1) - T(n-2,k-2), T(0,0) = 1, T(1,0) = 0, T(1,1) = 1, T(2,0) = 0, T(2,1) = 1, T(2,2) = 2, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Feb 12 2014
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EXAMPLE
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Triangle begins :
1
0, 1
0, 1, 2
0, 1, 3, 3
0, 1, 4, 6, 4
0, 1, 5, 10, 10, 5
0, 1, 6, 15, 20, 15, 6
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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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