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A201947
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Triangle T(n,k), read by rows, given by (1,1,-1,0,0,0,0,0,0,0,...) DELTA (1,-1,1,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938.
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1
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1, 1, 1, 2, 2, 0, 3, 5, 1, -1, 5, 10, 4, -2, -1, 8, 20, 12, -4, -4, 0, 13, 38, 31, -4, -13, -2, 1, 21, 71, 73, 3, -33, -11, 3, 1, 34, 130, 162, 34, -74, -42, 6, 6, 0, 55, 235, 344, 128, -146, -130, 0, 24, 3, -1
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OFFSET
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0,4
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COMMENTS
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Row-reversed variant of A123585. Row sums: 2^n.
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LINKS
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FORMULA
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G.f.: 1/(1-(1+y)*x+(y+1)*(y-1)*x^2).
T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) - T(n-2,k-2) with T(0,0)= 1 and T(n,k)= 0 if n<k or if k<0.
Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A090591(n), (-1)^n*A106852(n), A000007(n), A000045(n+1), A000079(n), A057083(n), A190966(n+1) for n = -3, -2, -1, 0, 1, 2, 3 respectively.
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EXAMPLE
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Triangle begins:
1
1, 1
2, 2, 0
3, 5, 1, -1
5, 10, 4, -2, -1
8, 20, 12, -4, -4, 0
13, 38, 31, -4, -13, -2, 1
21, 71, 73, 3, -33, -11, 3, 1
34, 130, 162, 34, -74, -42, 6, 6, 0
55, 235, 344, 128, -146, -130, 0, 24, 3, -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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