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A209150
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Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.
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2
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1, 2, 1, 4, 4, 1, 7, 10, 5, 1, 11, 21, 17, 7, 1, 16, 40, 46, 28, 8, 1, 22, 71, 107, 87, 39, 10, 1, 29, 119, 224, 232, 144, 55, 11, 1, 37, 190, 434, 555, 443, 226, 70, 13, 1, 46, 291, 792, 1221, 1198, 773, 328, 91, 14, 1, 56, 430, 1377, 2511, 2942, 2318, 1255
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OFFSET
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1,2
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COMMENTS
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Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...
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)=u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=x*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
2...1
4...4.....1
7...10....5....1
11...21...17...7...1
First three polynomials v(n,x): 1, 2 + x, 4 + 4x + x^2.
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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 + 1)*v[n - 1, x];
v[n_, x_] := 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]
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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