A290733 Number of compact partitions of n where each partition is counted with a certain weight.

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

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 A347277 A357734

Adjacent sequences: A290730 A290731 A290732 * A290734 A290735 A290736

Keyword

sign

Author

N. J. A. Sloane, Aug 10 2017

Status

approved