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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.)