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A210225
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Triangle of coefficients of polynomials u(n,x) jointly generated with A210226; see the Formula section.
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4
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1, 2, 1, 3, 5, 1, 4, 12, 10, 1, 5, 22, 36, 17, 1, 6, 35, 88, 87, 26, 1, 7, 51, 175, 277, 181, 37, 1, 8, 70, 306, 680, 734, 338, 50, 1, 9, 92, 490, 1416, 2196, 1710, 582, 65, 1, 10, 117, 736, 2632, 5402, 6156, 3606, 941, 82, 1, 11, 145, 1053, 4502, 11592
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OFFSET
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1,2
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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)+1,
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
2...1
3...5....1
4...12...10...1
5...22...36...17...1
First three polynomials u(n,x): 1, 2 + x, 3 + 5x + 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] + 1;
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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