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A209157
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Triangle of coefficients of polynomials v(n,x) jointly generated with A209154; see the Formula section.
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3
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1, 2, 2, 3, 6, 2, 4, 14, 12, 4, 5, 28, 40, 24, 4, 6, 50, 104, 96, 40, 8, 7, 82, 234, 304, 204, 72, 8, 8, 126, 476, 820, 768, 408, 112, 16, 9, 184, 896, 1968, 2408, 1760, 768, 192, 16, 10, 258, 1584, 4320, 6640, 6288, 3776, 1408, 288, 32, 11, 350, 2658
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OFFSET
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1,2
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COMMENTS
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Last number of each row is a power of 2.
(n-th alternating row sum)=2-n for n>1.
For a discussion and guide to related arrays, see A208510.
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LINKS
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FORMULA
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u(n,x)=u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=2x*u(n-1,x)+v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
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EXAMPLE
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First five rows:
1
2...2
3...6....2
4...14...12...4
5...28...40...24...4
First three polynomials v(n,x): 1, 2 + 2x, 3 + 6x + x^2.
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + v[n - 1, x] + 1;
Table[Expand[u[n, x]], {n, 1, z/2}]
Table[Expand[v[n, x]], {n, 1, z/2}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
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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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