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A208922
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Triangle of coefficients of polynomials v(n,x) jointly generated with A208921; see the Formula section.
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3
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1, 3, 1, 5, 4, 2, 7, 13, 12, 2, 9, 32, 40, 16, 4, 11, 65, 108, 80, 36, 4, 13, 116, 258, 288, 180, 48, 8, 15, 189, 560, 842, 700, 324, 96, 8, 17, 288, 1120, 2144, 2312, 1536, 640, 128, 16, 19, 417, 2088, 4944, 6728, 5832, 3232, 1088, 240, 16, 21, 580, 3666
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OFFSET
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1,2
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COMMENTS
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Alternating row sums: 1,2,3,4,5,6,7,8,9,10,...
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)+2x*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
3...1
5...4....2
7...13...12...2
9...32...40...16...4
First five polynomials v(n,x):
1
3 + x
5 + 4x + 2x^2
7 + 13x + 12x^2 + 2x^3
9 + 32x + 40x^2 + 16x^3 + 4x^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] + 2x*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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STATUS
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approved
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