Loop using the output from previous row as variable

There are several  ways to do this. Here's a method using the List.Generate function:

let
    Source = Table.FromRows(Json.Document(Binary.Decompress(Binary.FromText("i45WMlTSUTI0ABKmQGyuFKsTrWQEZBkghEFCxlAhkCJDI7CQCVTIAqIoFgA=", BinaryEncoding.Base64), Compression.Deflate)), let _t = ((type nullable text) meta [Serialized.Text = true]) in type table [WEEK = _t, INITIAL = _t, IN = _t, OUT = _t]),
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"WEEK", Int64.Type}, 
        {"INITIAL", Int64.Type}, {"IN", Int64.Type}, {"OUT", Int64.Type}}),

    #"Add New Initial" = 
        Table.FromColumns(
            Table.ToColumns(#"Changed Type") &
                {List.Generate(
                    ()=>[a=#"Changed Type"[INITIAL]{0}, idx=0],
                    each [idx] < Table.RowCount(#"Changed Type"),
                    each [a = [a]+#"Changed Type"[IN]{[idx]} - #"Changed Type"[OUT]{[idx]}, idx=[idx]+1],
                    each [a])},
            type table[WEEK=Int64.Type,INITIAL=Int64.Type, IN=Int64.Type, OUT=Int64.Type, NEW_INITIAL=Int64.Type]),
    
    #"Reordered Columns" = Table.ReorderColumns(#"Add New Initial",{"WEEK", "INITIAL", "NEW_INITIAL", "IN", "OUT"})
in
    #"Reordered Columns"

Source

Results

You would use the same method, just embed it as an aggregation in the Table.Group function:

let
    Source = Excel.CurrentWorkbook(){[Name="Table3"]}[Content],
    #"Changed Type" = Table.TransformColumnTypes(Source,{{"WEEK", Int64.Type}, {"PRODUCT ID", Int64.Type}, {"INITIAL", Int64.Type}, {"IN", Int64.Type}, {"OUT", Int64.Type}}),
    
    #"Grouped Rows" = Table.Group(#"Changed Type", {"PRODUCT ID"}, {
        {"New Initial", (t)=>              
          Table.FromColumns(
            Table.ToColumns(t) &
                {List.Generate(
                    ()=>[a=t[INITIAL]{0}, idx=0],
                    each [idx] < Table.RowCount(t),
                    each [a = [a] + t[IN]{[idx]} - t[OUT]{[idx]}, idx=[idx]+1],
                    each [a])},
                    Table.ColumnNames(t) & {"NEW INITIAL"}),
            type table[WEEK=Int64.Type,PRODUCT ID=Int64.Type, INITIAL=Int64.Type, 
                            IN=Int64.Type, OUT=Int64.Type, NEW INITIAL=Int64.Type]}}),

    #"Expanded New Initial" = Table.ExpandTableColumn(#"Grouped Rows", "New Initial", {"WEEK", "INITIAL", "IN", "OUT", "NEW INITIAL"})
in
    #"Expanded New Initial"