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A208516
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Triangle of coefficients of polynomials u(n,x) jointly generated with A208517; see the Formula section.
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3
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1, 1, 1, 1, 2, 3, 1, 3, 6, 7, 1, 4, 9, 15, 17, 1, 5, 12, 24, 39, 41, 1, 6, 15, 34, 66, 100, 99, 1, 7, 18, 45, 98, 178, 256, 239, 1, 8, 21, 57, 135, 276, 478, 653, 577, 1, 9, 24, 70, 177, 395, 772, 1275, 1661, 1393, 1, 10, 27, 84, 224, 536, 1145, 2139, 3383, 4214
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OFFSET
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1,5
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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)=x*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...1
1...2...3
1...3...6...7
1...4...9...15...17
First five polynomials u(n,x):
1
1 + x
1 + 2x + 3x^2
1 + 3x + 6x^2 + 7x^3
1 + 4x + 9x^2 + 15x^3 + 17x^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_] := 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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