cp's OEIS Frontend

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

%I A290733 #18 Dec 18 2023 12:11:41
%S A290733 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,
%T A290733 -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,
%U A290733 3,2,-6,-6,-5,-4,4,2,-2
%N A290733 Number of compact partitions of n where each partition is counted with a certain weight.
%C A290733 See Andrews (2016) for the definition of the particular weight used here.
%C A290733 4*a(n) + 2*A290734(n) = (-1)^n*A005875(n) for n > 0.
%H A290733 George E. Andrews, <a href="https://georgeandrews1.github.io/pdf/320.pdf">The Bhargava-Adiga Summation and Partitions</a>, 2016. See Lemma 2.1.
%F A290733 See Maple program for g.f.
%p A290733 M:=101;
%p A290733 B:=proc(a,q,n) local j,t1; global M;
%p A290733 t1:=1;
%p A290733 for j from 0 to M do
%p A290733 t1:=t1*(1-a*q^j)/(1-a*q^(n+j));
%p A290733 od;
%p A290733 t1; end;
%p A290733 # c_0
%p A290733 t2:=add((-1)^m*q^m*B(-q,q,m-1)/(1+q^m), m=1..M):
%p A290733 series(t2,q,M);
%p A290733 seriestolist(%);
%Y A290733 Cf. A005875, A290734.
%K A290733 sign
%O A290733 0,3
%A A290733 _N. J. A. Sloane_, Aug 10 2017