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A210795
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Triangle of coefficients of polynomials u(n,x) jointly generated with A210796; see the Formula section.
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3
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1, 2, 1, 3, 2, 2, 4, 5, 5, 3, 5, 8, 12, 9, 5, 6, 13, 22, 25, 17, 8, 7, 18, 38, 51, 51, 31, 13, 8, 25, 59, 98, 115, 101, 56, 21, 9, 32, 88, 166, 238, 248, 196, 100, 34, 10, 41, 124, 270, 438, 552, 520, 374, 177, 55, 11, 50, 170, 410, 762, 1090, 1234, 1064, 704
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OFFSET
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1,2
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COMMENTS
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Row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
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*v(n-1,x)+1,
v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
where u(1,x)=1, v(1,x)=1.
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EXAMPLE
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First five rows:
1
2...1
3...2...2
4...5...5....3
5...8...12...9...5
First three polynomials u(n,x): 1, 2 + x, 3 + 2x + 2x^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 + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 1; h = 2; p = -1; f = 0;
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]
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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