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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

Alois P. Heinz, Rows n = 0..1500, flattened

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: A265271 A006020 A294177 * A190704 A190698 A283183

Adjacent sequences:  A224378 A224379 A224380 * A224382 A224383 A224384

KEYWORD

nonn,look,tabf

AUTHOR

Philippe Deléham, Apr 05 2013

STATUS

approved

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Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)