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A290733
Number of compact partitions of n where each partition is counted with a certain weight.
7
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
OFFSET
0,3
COMMENTS
See Andrews (2016) for the definition of the particular weight used here.
4*a(n) + 2*A290734(n) = (-1)^n*A005875(n) for n > 0.
LINKS
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
Sequence in context: A215062 A215063 A316781 * A113020 A347277 A357734
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Aug 10 2017
STATUS
approved