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A224381
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Table of coefficients in the expansion of product((1+d_i*x), d_i|n).
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4
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1, 1, 1, 1, 3, 2, 1, 4, 3, 1, 7, 14, 8, 1, 6, 5, 1, 12, 47, 72, 36, 1, 8, 7, 1, 15, 70, 120, 64, 1, 13, 39, 27, 1, 18, 97, 180, 100, 1, 12, 11, 1, 28, 287, 1400, 3444, 4032, 1728, 1, 14, 13, 1, 24, 163, 336, 196, 1, 24, 158, 360, 225, 1, 31, 310, 1240, 1984, 1024
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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Alois P. Heinz, Rows n = 0..1500, flattened
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FORMULA
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T(n,k) = [x^k] Product_{d|n} (1+d*x).
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EXAMPLE
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Row n = 6 : 1, 12, 47, 72, 36 because (1+x)*(1+2x)*(1+3x)*(1+6x) = 1 + 12*x + 47*x^2 + 72*x^3 + 36*x^4.
Table begins :
1
1, 1
1, 3, 2
1, 4, 3
1, 7, 14, 8
1, 6, 5
1, 12, 47, 72, 36
1, 8, 7
1, 15, 70, 120, 64
1, 13, 39, 27
1, 18, 97, 180, 100
1, 12, 11
1, 28, 287, 1400, 3444, 4032, 1728
1, 14, 13
1, 24, 163, 336, 196
1, 24, 158, 360, 225
1, 31, 310, 1240, 1984, 1024
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MAPLE
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with(numtheory):
T:= proc(n) local p;
p:= mul(1+d*x, d=divisors(n));
seq(coeff(p, x, k), k=0..degree(p))
end:
seq(T(n), n=0..30); # Alois P. Heinz, Apr 05 2013
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MATHEMATICA
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T[n_] := CoefficientList[Product[1+d*x, {d, Divisors[n]}], x]; T[0] = {1};
Array[T, 20, 0] // Flatten (* Jean-François Alcover, Mar 27 2017 *)
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CROSSREFS
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Columns k=0-3 give: A000012, A000203, A119616, A067817.
Row lengths are: A000005(n)+1.
Last elements of rows give: A007955.
Sequence in context: A265271 A006020 A294177 * A190704 A190698 A283183
Adjacent sequences: A224378 A224379 A224380 * A224382 A224383 A224384
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KEYWORD
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nonn,look,tabf
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AUTHOR
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Philippe Deléham, Apr 05 2013
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STATUS
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approved
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