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A208509
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Triangle of coefficients of polynomials v(n,x) jointly generated with A208508; see the Formula section.
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4
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1, 3, 5, 1, 7, 5, 9, 14, 1, 11, 30, 7, 13, 55, 27, 1, 15, 91, 77, 9, 17, 140, 182, 44, 1, 19, 204, 378, 156, 11, 21, 285, 714, 450, 65, 1, 23, 385, 1254, 1122, 275, 13, 25, 506, 2079, 2508, 935, 90, 1, 27, 650, 3289, 5148, 2717, 442, 15, 29, 819, 5005, 9867
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OFFSET
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1,2
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COMMENTS
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col 1: A005408
col 2: A000330 (square pyramidal numbers)
col 3: A005585
col 4: A050486
col 5: A054333
col 6: A057788
row sums, v(n,1): A003948
alternating row sums, v(n,-1): A090131
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LINKS
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Table of n, a(n) for n=1..60.
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FORMULA
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u(n,x)=u(n-1,x)+x*v(n-1,x),
v(n,x)=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
5...1
7...5
9...14...1
First five polynomials v(n,x):
1
3
5 + x
7 + 5x
9 + 14x + x^2
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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_] := 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]
Flatten[%] (* A208508 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208509 *)
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CROSSREFS
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Cf. A208508.
Sequence in context: A202356 A152204 A114216 * A086233 A065395 A197326
Adjacent sequences: A208506 A208507 A208508 * A208510 A208511 A208512
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KEYWORD
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nonn,tabf
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AUTHOR
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Clark Kimberling, Feb 27 2012
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STATUS
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approved
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