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.
0, 1, 2, 6, 11, 22, 40, 72, 120, 203, 331, 526, 828, 1277, 1947, 2931, 4372
Offset: 1
Crossrefs
Cf. A000569.
Programs
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Maple
K:=1 product((1+z*q*q^j)^k*(1+z^-1*x^j)^k, j=0..40): series(%,q,35): convert(%,polynom): expand(%): A:=coeff(%,z,0): for m from 2 by 2 to 40 do for i to m do f(m):=add(coeff(coeff(A,x,i),q,m-i),i=m/2..m); end do; for n from 2 by 2 to 40 do a(n):=f(n)-coeff(coeff(A,q,n/2),x,n/2); end do
Formula
a(n) <= A000569(n).