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A209578
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Triangle of coefficients of polynomials v(n,x) jointly generated with A209577; see the Formula section.
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3
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1, 3, 1, 5, 3, 1, 9, 8, 4, 1, 15, 19, 13, 5, 1, 25, 41, 36, 19, 6, 1, 41, 84, 90, 60, 26, 7, 1, 67, 165, 210, 169, 92, 34, 8, 1, 109, 315, 465, 439, 287, 133, 43, 9, 1, 177, 588, 990, 1073, 818, 454, 184, 53, 10, 1, 287, 1079, 2043, 2502, 2178, 1405, 681, 246
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OFFSET
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1,2
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COMMENTS
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Alternating row sums: 1,0,2,1,3,2,4,3,5,4,... (A028242).
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),
v(n,x)=(x+1)*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...1
3...2....1
5...6....3....1
9...13...10...4...1
First three polynomials v(n,x): 1, 1 + x , 3 + 2x + 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];
v[n_, x_] := (x + 1)*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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