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A209701
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Triangle of coefficients of polynomials u(n,x) jointly generated with A209702; see the Formula section.
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3
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1, 0, 2, 0, 2, 5, 0, 3, 7, 12, 0, 4, 11, 23, 29, 0, 5, 16, 41, 70, 70, 0, 6, 22, 66, 140, 204, 169, 0, 7, 29, 99, 247, 455, 577, 408, 0, 8, 37, 141, 401, 875, 1423, 1597, 985, 0, 9, 46, 193, 613, 1529, 2965, 4321, 4348, 2378, 0, 10, 56, 256, 895, 2495, 5549
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OFFSET
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1,3
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COMMENTS
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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)=x*u(n-1,x)+x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+(x+1)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
0...2
0...2...5
0...3...7....12
0...4...11...23...29
First three polynomials v(n,x): 1, 2x, 2x + 5x^2.
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + (x + 1)*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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