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A207617
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Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; see the Formula section.
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3
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1, 2, 1, 3, 3, 4, 7, 1, 5, 14, 5, 6, 25, 16, 1, 7, 41, 41, 7, 8, 63, 91, 29, 1, 9, 92, 182, 92, 9, 10, 129, 336, 246, 46, 1, 11, 175, 582, 582, 175, 11, 12, 231, 957, 1254, 550, 67, 1, 13, 298, 1507, 2508, 1507, 298, 13, 14, 377, 2288, 4719, 3718, 1079, 92, 1
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OFFSET
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1,2
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LINKS
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FORMULA
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u(n,x)=u(n-1,x)+v(n-1,x), v(n,x)=xu(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
3...3
4...7...1
5...14...5
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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] + v[n - 1, x]
v[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
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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nonn,tabf
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AUTHOR
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STATUS
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approved
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