What is clearest is 'Han makibari' 半巻張 ie half of the barrel is twist/bound.
The place is probably Kunitomo Ju 国友住 but only the bottom line of the last character is visible. (Educated guess)
The name is poorly written but seems to be Toku Uemon Saku 徳右衛門 作
Toku Uemon was a known Kunitomo smith.
Def looks like it got some years on it. Even the pan has been repaired from all the useage.
This Han maki-bari is a new term to me. We have maki bari=single wrap, Ni ju maki-bari=double wrap and So maki-bari=trippel wrap and over.
Was the Han maki-bari the first step from the none wrapped "Udon-guns" towards the more standard maki-bari? Or was it just one way of making these guns "for the mass ranks" less expensive and faster to produce? Which part of the barrel would have been strengthen?
Hardly any Kunitomo smiths used the word Ju (living in). Perhaps five out of many hundreds. Two or three of these are dated, in the 1600s.
Jan is probably right over the meaning of Han makibari, when the process of binding and forging was still early, and/or expensive.
Toku was probably first used to show respect to the new Tokugawa Shogun. How long did that fashion last? Your smith has scribbled it, though, as if it had become less fresh. Smiths often used Left or Right in their names in the earlier years. I have a gun by a Tokusaemon, identical to the name of your smith, if you just replace Sa (left) for U (right). He was active from about 1580 to 1620.
So you can see that the reasoning is circumstantial...