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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

Table of n, a(n) for n=0..64.

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.)