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A208606
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Triangle of coefficients of polynomials u(n,x) jointly generated with A208607; see the Formula section.
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3
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1, 1, 1, 1, 4, 1, 1, 9, 4, 1, 1, 16, 12, 7, 1, 1, 25, 30, 26, 7, 1, 1, 36, 65, 73, 32, 10, 1, 1, 49, 126, 175, 113, 52, 10, 1, 1, 64, 224, 378, 332, 199, 61, 13, 1, 1, 81, 372, 756, 852, 634, 277, 87, 13, 1, 1, 100, 585, 1422, 1974, 1779, 1024, 421, 99, 16, 1, 1, 121
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OFFSET
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1,5
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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+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
1...4....1
1...9....4....1
1...16...12...7...1
First five polynomials u(n,x):
1
1 + x
1 + 4x + 1x^2
1 + 9x + 4x^2 + x^3
1 + 16x + 12x^2 + 7x^3 + x^4
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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*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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EXTENSIONS
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STATUS
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approved
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