login
A290734
Number of compact partitions of n containing a 1 where each partition is counted with a certain weight.
5
0, -1, 2, -2, 3, -6, 6, -4, 6, -9, 10, -8, 6, -12, 14, -6, 7, -16, 16, -8, 10, -18, 14, -8, 8, -17, 24, -10, 6, -24, 22, -4, 10, -22, 20, -16, 9, -20, 28, -6, 8, -32, 26, -8, 14, -28, 24, -8, 8, -25, 34, -18, 6, -36, 34, -2, 18, -28, 24, -24, 10, -28, 40, -4, 7, -42, 38, -12, 18, -40, 26, -12, 12, -28
OFFSET
0,3
COMMENTS
See Andrews (2016) for the definition of the particular weight used here.
4*A290733(n) + 2*a(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_1
T1:=add( (-1)^m*q^(m*(m+1)/2)/(B(-q, q, m)*(1+q^m)), m=1..M):
series(T1, q, M); c1seq:=seriestolist(%);
CROSSREFS
Sequence in context: A070871 A096115 A289838 * A093919 A179661 A178888
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Aug 10 2017
STATUS
approved