gf := n -> exp(n*(arctanh(z)/z + 1/2*log(-z^2 + 1) - 1));
ser := n -> series(gf(n), z, n + 2);
g := n -> ilcm(seq(denom(coeff(ser(n), z, k)), k = 0 .. n));
f := proc(n, m) coeff(ser(n), z, m); end proc;
cc := proc(n) local vv, m; if 0 = n mod 2 then vv := seq(g(n)*f(n, n-m), m = 0 .. n); end if; if 1 = n mod 2 then vv := seq(g(n)*f(n, n-m), m = 0 .. n); end if; vv; end proc;
for i from 0 to 10 do cc(i); end do;