You will eliminate one step of the double crochet to make this stitch. Chain an even number of stitches. Place yarn over hook. Insert the hook into the 3rd chain from hook and draw a loop through. You will have 3 loops on the hook. Hook the yarn and draw it through all 3 loops on hook. This completes one half double crochet.

Source: Christmas Time Crochet, Craft Publications Volume 7317
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This video will show you how to crochet a half double crochet.
How to work half double crochet - "hdc"
Ch required length.
Step 1 - Y O, insert hook into 3rd ch from hook, draw yarn through - 3 loops on hook -. Draw through all 3 loops; one half double crochet made. Work 1 hdc in each remaining ch.

Step 2 - Ch 2 turn, work 1 hdc in first st from hook and each remaining st, inserting hook under both strands of st unless otherwise specified.
Repeat step 2 for desired number of rows.
Source: Crochet Primer, Bernhard Ulmann Volume 64