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A209159
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Triangle of coefficients of polynomials v(n,x) jointly generated with A209158; see the Formula section.
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3
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1, 1, 3, 1, 5, 5, 1, 7, 15, 11, 1, 9, 29, 41, 21, 1, 11, 47, 99, 103, 43, 1, 13, 69, 193, 301, 249, 85, 1, 15, 95, 331, 687, 851, 583, 171, 1, 17, 125, 521, 1349, 2225, 2285, 1337, 341, 1, 19, 159, 771, 2391, 4923, 6735, 5907, 3015, 683, 1, 21, 197, 1089
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OFFSET
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1,3
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COMMENTS
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Alternating row sums: 1,-2,1,-2,1,-2,1,-2,1,-2,...
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)=2x*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...3
1...5...5
1...7...15...11
1...9...29...41...21
First three polynomials v(n,x): 1, 1 + 3x, 1 + 5x + 5x^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_] := 2 x*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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