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MAPLE
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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
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