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A236376
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Riordan array ((1-x+x^2)/(1-x)^2, x/(1-x)^2).
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1
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1, 1, 1, 2, 3, 1, 3, 7, 5, 1, 4, 14, 16, 7, 1, 5, 25, 41, 29, 9, 1, 6, 41, 91, 92, 46, 11, 1, 7, 63, 182, 246, 175, 67, 13, 1, 8, 92, 336, 582, 550, 298, 92, 15, 1, 9, 129, 582, 1254, 1507, 1079, 469, 121, 17, 1, 10, 175, 957, 2508, 3718, 3367, 1925, 696, 154
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OFFSET
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0,4
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COMMENTS
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Triangle T(n,k), read by rows, given by (1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 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 - x + x^2)/(1 - 2*x - x*y + x^2).
T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = 2, T(2,1) = 3, T(2,2) = 1, T(n,k) = 0 if k < 0 or k > n.
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EXAMPLE
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Triangle begins:
1;
1, 1;
2, 3, 1;
3, 7, 5, 1;
4, 14, 16, 7, 1;
5, 25, 41, 29, 9, 1;
6, 41, 91, 92, 46, 11, 1;
7, 63, 182, 246, 175, 67, 13, 1;
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MAPLE
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# The function RiordanSquare is defined in A321620.
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MATHEMATICA
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CoefficientList[#, y] & /@
CoefficientList[
Series[(1 - x + x^2)/(1 - 2*x - x*y + x^2), {x, 0, 12}], x] (* Wouter Meeussen, Jan 25 2014 *)
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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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