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A209579
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Triangle of coefficients of polynomials u(n,x) jointly generated with A209580; see the Formula section.
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3
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1, 1, 1, 2, 3, 1, 2, 6, 6, 1, 3, 9, 14, 10, 1, 3, 14, 28, 29, 15, 1, 4, 18, 48, 71, 55, 21, 1, 4, 25, 75, 139, 158, 97, 28, 1, 5, 30, 112, 251, 356, 321, 161, 36, 1, 5, 39, 156, 413, 724, 828, 609, 254, 45, 1, 6, 45, 215, 645, 1321, 1874, 1782, 1094, 384, 55, 1, 6
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OFFSET
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1,4
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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)+v(n-1,x),
v(n,x)=(x+1)*u(n-1,x)+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
1...1
2...3....1
2...6....6....1
3...9....14...10...1
First three polynomials v(n,x): 1, 1 + x, 2 + 3x + x^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] + v[n - 1, x];
v[n_, x_] := (x + 1)*u[n - 1, x] + 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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