How to pass a path variable through API Gateway

This is what I currently have in my Swagger file:

"/v1/user/{username}": {
      "get": {
        "consumes": ["application/json"],
        "produces": ["application/json"],
        "parameters": [{
          "name": "username",
          "in": "path",
          "description": "Username of user",
          "required": true,
          "type": "string"
        }],
        "responses": {
          "200": {
            "description": "user retrieved",
            "schema": {
              "type": "array",
              "items": {
                "$ref": "#/definitions/User"
              }
            }
          }
        },
        "x-amazon-apigateway-integration": {
          "type": "http",
          "uri": "http://useroregon.recopspipeline.com/v1/user/{username}",
          "httpMethod": "GET",
          "responses": {
            "default": {
              "statusCode": "200",
              "responseTemplates": {
                "application/json": "$input.json('$.body')"
              }
            }
          }
        }
      },

But my backend just receives "{username}" as the path variable.
Anyone know how to send the path variable along?
Tips on how to do it in a swagger json file or via the GUI would be great!

Solution

This OpenAPI (fka. Swagger) file miss the mapping between request parameter and proxied service (requestParameters in x-amazon-apigateway-integration).

 "x-amazon-apigateway-integration": {
      "type": "http",
      "uri": "http://useroregon.recopspipeline.com/v1/user/{username}",
      "requestParameters": {
        "integration.request.path.username": "method.request.path.username"
      }
      "httpMethod": "GET",
      "responses": {
        "default": {
          "statusCode": "200",
          "responseTemplates": {
            "application/json": "$input.json('$.body')"
          }
        }
      }
    }

If you design your API with a proxy operation using the API Gateway console and exporting it you get this:

swagger: "2.0"
info:
  title: "Proxy"

schemes:
- "https"

paths:
  /test/{username}:
    get:
      produces:
      - "application/json"
      parameters:
      - name: "username"
        in: "path"
        required: true
        type: "string"
      responses:
        200:
          description: "200 response"
          schema:
            $ref: "#/definitions/Empty"
      x-amazon-apigateway-integration:
        responses:
          default:
            statusCode: "200"
        requestParameters:
          integration.request.path.username: "method.request.path.username"
        passthroughBehavior: "when_no_match"
        httpMethod: "GET"
        uri: "http://somedomain.com/{username}"
        type: "http"

definitions:
  Empty:
    type: "object"

Your definition lacks also passthroughBehavior: "when_no_match" but it may not be a problem.