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A208526
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Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.
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3
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1, 1, 1, 1, 2, 4, 1, 3, 8, 10, 1, 4, 12, 22, 28, 1, 5, 16, 36, 68, 76, 1, 6, 20, 52, 120, 200, 208, 1, 7, 24, 70, 184, 376, 592, 568, 1, 8, 28, 90, 260, 608, 1184, 1736, 1552, 1, 9, 32, 112, 348, 900, 2016, 3672, 5072, 4240, 1, 10, 36, 136, 448, 1256, 3120
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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)=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...1
1...2...4
1...3...8....10
1...4...12...22...28
First five polynomials u(n,x):
1
1 + x
1 + 2x + 4x^2
1 + 3x + 8x^2 + 10x^3
1 + 4x + 12x^2 + 22x^3 + 28x^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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