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A224381 Table of coefficients in the expansion of product((1+d_i*x), d_i|n). 4
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)
OFFSET
0,5
LINKS
FORMULA
T(n,k) = [x^k] Product_{d|n} (1+d*x).
EXAMPLE
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;
...
MAPLE
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
MATHEMATICA
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 *)
CROSSREFS
Columns k=0-3 give: A000012, A000203, A119616, A067817.
Row lengths are: A000005(n)+1.
Last elements of rows give: A007955.
Sequence in context: A350499 A006020 A294177 * A190704 A346611 A190698
KEYWORD
nonn,look,tabf
AUTHOR
Philippe Deléham, Apr 05 2013
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)