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A210041
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Triangle of coefficients of polynomials u(n,x) jointly generated with A209758; see the Formula section.
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3
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1, 3, 5, 3, 7, 8, 6, 9, 15, 19, 12, 11, 24, 41, 44, 24, 13, 35, 74, 107, 100, 48, 15, 48, 120, 214, 270, 224, 96, 17, 63, 181, 380, 591, 664, 496, 192, 19, 80, 259, 622, 1137, 1576, 1600, 1088, 384, 21, 99, 356, 959, 2001, 3259, 4088, 3792, 2368, 768, 23
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OFFSET
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1,2
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COMMENTS
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Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...
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)+v(n-1,x)+1,
v(n,x)=x*u(n-1,x)+2x*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
3
5...3
7...8....6
9...15...19...12
First three polynomials u(n,x): 1, 3, 5 + 3x.
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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] + 1;
v[n_, x_] := x*u[n - 1, x] + 2 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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nonn,tabf
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AUTHOR
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STATUS
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approved
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