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A208612
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Triangle of coefficients of polynomials u(n,x) jointly generated with A208613; see the Formula section.
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3
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1, 1, 1, 1, 4, 2, 1, 9, 9, 3, 1, 16, 26, 19, 5, 1, 25, 60, 70, 38, 8, 1, 36, 120, 197, 167, 73, 13, 1, 49, 217, 469, 553, 375, 137, 21, 1, 64, 364, 994, 1528, 1427, 803, 252, 34, 1, 81, 576, 1932, 3714, 4476, 3449, 1661, 457, 55, 1, 100, 870, 3510, 8196
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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)+(x+1)*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....2
1...9....9....3
1...16...26...19...5
First five polynomials u(n,x):
1
1 + x
1 + 4x + 2x^2
1 + 9x + 9x^2 + 3x^3
1 + 16x + 26x^2 + 19x^3 + 5x^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] + (x + 1)*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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