f := (1-t)*(1-s)*(1-u)/(1-2*(s+t+u)+3*(s*t+t*u+u*s)-4*s*t*u):
truncate := proc(f, v, prec, $)
  convert(series(f, v, prec), polynom)
end proc:
central_coeff := proc(S, k, $)
  coeff(coeff(coeff(S, t, k), s, k), u, k)
end proc:
prec := 25:
S := truncate(truncate(truncate(f, t, prec), s, prec), u, prec):
fs := add(central_coeff(S, k) * T^k, k=0..prec-1);
rec := gfun:-seriestorec(series(fs, T, prec-1), a(n))[1];
bn := map(factor, 70 * eval(rec[1], n=n-3));
collect(bn + 6 * eval(bn, n=n-1), a, factor);
collect(%/(35*n-52), a, factor);