cp's OEIS Frontend

A363936 Number of Frobenius partitions of 2n wherein the number of columns plus the weight on the top row is strictly less than the weight on the bottom row.

%I A363936 #118 Aug 02 2023 14:31:59
%S A363936 0,1,2,6,11,22,40,72,120,203,331,526,828,1277,1947,2931,4372
%N A363936 Number of Frobenius partitions of 2n wherein the number of columns plus the weight on the top row is strictly less than the weight on the bottom row.
%F A363936 a(n) <= A000569(n).
%p A363936 K:=1
%p A363936 product((1+z*q*q^j)^k*(1+z^-1*x^j)^k, j=0..40):
%p A363936 series(%,q,35):
%p A363936 convert(%,polynom):
%p A363936 expand(%):
%p A363936 A:=coeff(%,z,0):
%p A363936 for m from 2 by 2 to 40 do
%p A363936 for i to m do f(m):=add(coeff(coeff(A,x,i),q,m-i),i=m/2..m);
%p A363936 end do;
%p A363936 for n from 2 by 2 to 40 do
%p A363936 a(n):=f(n)-coeff(coeff(A,q,n/2),x,n/2); end do
%Y A363936 Cf. A000569.
%K A363936 nonn,more
%O A363936 1,3
%A A363936 _Kelsey A. Blum_, Jul 09 2023