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A210754
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Triangle of coefficients of polynomials v(n,x) jointly generated with A210753; see the Formula section.
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4
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1, 3, 2, 6, 9, 4, 10, 25, 24, 8, 15, 55, 85, 60, 16, 21, 105, 231, 258, 144, 32, 28, 182, 532, 833, 728, 336, 64, 36, 294, 1092, 2241, 2720, 1952, 768, 128, 45, 450, 2058, 5301, 8361, 8280, 5040, 1728, 256, 55, 660, 3630, 11385, 22363, 28610, 23920
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OFFSET
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1,2
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COMMENTS
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Column 1: triangular numbers, A2000217
Coefficient of v(n,x): 2^(n-1)
Row sums: A035344
Alternating row sums: 1,1,1,1,1,1,1,1,1,...
For a discussion and guide to related arrays, see A208510.
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LINKS
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Table of n, a(n) for n=1..52.
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FORMULA
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u(n,x)=(x+1)*u(n-1,x)+x*v(n-1,x)+1,
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
3....2
6....9....4
10...25...24...8
15...55...85...60...16
First three polynomials v(n,x): 1, 3 + 2x, 6 + 9x +4x^2
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MATHEMATICA
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u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := (x + 1)*u[n - 1, x] + x*v[n - 1, x] + 1;
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]
Flatten[%] (* A210753 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210754 *)
Table[u[n, x] /. x -> 1, {n, 1, z}] (* A007070 *)
Table[v[n, x] /. x -> 1, {n, 1, z}] (* A035344 *)
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CROSSREFS
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Cf. A210753, A208510.
Sequence in context: A131006 A122362 A072635 * A210738 A210601 A197493
Adjacent sequences: A210751 A210752 A210753 * A210755 A210756 A210757
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Mar 25 2012
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STATUS
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approved
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