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A210867
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Triangle of coefficients of polynomials v(n,x) jointly generated with A210866; see the Formula section.
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4
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1, 2, 1, 3, 5, 2, 4, 15, 12, 3, 5, 34, 51, 28, 5, 6, 65, 170, 156, 60, 8, 7, 111, 465, 680, 438, 126, 13, 8, 175, 1092, 2465, 2411, 1145, 255, 21, 9, 260, 2282, 7623, 10968, 7805, 2854, 506, 34, 10, 369, 4356, 20608, 42735, 43440, 23509, 6813, 984, 55
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OFFSET
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1,2
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COMMENTS
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For n>1, row n starts with n and ends with F(n), where F=A000045 (Fibonacci numbers).
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*v(n-1,x),
v(n,x)=(x+n)*u(n-1,x)+x*v(n-1,x)-x,
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....2
4...15...12...3
5...34...51...28...5
First three polynomials v(n,x): 1, 2 + x, 3 + 5x + 2x^2
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 14;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := (x + n)*u[n - 1, x] + x*v[n - 1, x] - x;
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]
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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