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A208527
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Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.
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3
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1, 1, 4, 1, 4, 10, 1, 4, 12, 28, 1, 4, 14, 40, 76, 1, 4, 16, 52, 124, 208, 1, 4, 18, 64, 176, 384, 568, 1, 4, 20, 76, 232, 592, 1168, 1552, 1, 4, 22, 88, 292, 832, 1936, 3520, 4240, 1, 4, 24, 100, 356, 1104, 2880, 6240, 10512, 11584, 1, 4, 26, 112, 424, 1408
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OFFSET
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1,3
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LINKS
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FORMULA
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u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+2x*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
1...4
1...4...10
1...4...12...28
1...4...14...40...76
First five polynomials v(n,x):
1
1 + 4x
1 + 4x + 10x^2
1 + 4x + 12x^2 + 28x^3
1 + 4x + 14x^2 + 40x^3 + 76x^4
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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*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 2 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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