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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
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OFFSET
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0,5
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LINKS
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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:
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MATHEMATICA
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T[n_] := CoefficientList[Product[1+d*x, {d, Divisors[n]}], x]; T[0] = {1};
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CROSSREFS
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Last elements of rows give: A007955.
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KEYWORD
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AUTHOR
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STATUS
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approved
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