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 A290733 Number of compact partitions of n where each partition is counted with a certain weight. 8
 0, -1, 2, -1, 0, -3, 3, 2, 0, -3, 1, -2, -1, 0, 5, 3, -2, -4, 1, -2, 1, -3, -1, 4, 2, 1, 6, -3, -3, -6, 1, 2, -2, -1, 2, -4, 3, 4, 4, 3, 2, -8, -1, -2, -1, -4, 0, 4, -2, -1, 4, -3, 3, 0, 7, 1, 3, 2, -6, -6, -5, -4, 4, 2, -2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See Andrews (2016) for the definition of the particular weight used here. 4*A290733(n) + 2*A290734(n) = (-1)^n*A005875(n) for n > 0. LINKS George E. Andrews, The Bhargava-Adiga Summation and Partitions, 2016. See Lemma 2.1. FORMULA See Maple program for g.f. MAPLE M:=101; B:=proc(a, q, n) local j, t1; global M; t1:=1; for j from 0 to M do t1:=t1*(1-a*q^j)/(1-a*q^(n+j)); od; t1; end; # c_0 t2:=add((-1)^m*q^m*B(-q, q, m-1)/(1+q^m), m=1..M): series(t2, q, M); seriestolist(%); CROSSREFS Cf. A005875, A290734. Sequence in context: A215062 A215063 A316781 * A113020 A228821 A127258 Adjacent sequences:  A290730 A290731 A290732 * A290734 A290735 A290736 KEYWORD sign AUTHOR N. J. A. Sloane, Aug 10 2017 STATUS approved

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Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)