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| NAME
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allocatedTriangle of coefficients of polynomials u(n,x) jointly generated with A208914; see forthe ClarkFormula Kimberlingsection.
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| DATA
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1, 1, 2, 1, 6, 4, 1, 12, 12, 8, 1, 20, 24, 40, 16, 1, 30, 40, 120, 80, 32, 1, 42, 60, 280, 240, 224, 64, 1, 56, 84, 560, 560, 896, 448, 128, 1, 72, 112, 1008, 1120, 2688, 1792, 1152, 256, 1, 90, 144, 1680, 2016, 6720, 5376, 5760, 2304, 512, 1, 110, 180
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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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| FORMULA
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u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=2x*u(n-1,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...2
1...6....4
1...12...12...8
1...20...24...40...16
First five polynomials u(n,x):
1
1 + 2x
1 + 6x + 4x^2
1 + 12x + 12x^2 + 8x^3
1 + 20x + 24x^2 + 40x^3 + 16x^4
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| MATHEMATICA
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u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, 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]
Flatten[%] (* A208913 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208914 *)
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| CROSSREFS
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Cf. A208914, A208510.
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| KEYWORD
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allocated
nonn,tabl
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| AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Mar 03 2012
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| STATUS
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approved
editing
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