CREATE TABLE [dbo].[table] (
      tableID [int] IDENTITY(1,1) NOT NULL
    , DatumCreate [datetime] DEFAULT GetDate() NOT NULL,
    , other values ....
    , CONSTRAINT pk_FactuurID PRIMARY KEY (FactuurID)
    )
GO

CREATE TRIGGER my_trigger
   ON  my_table
   AFTER INSERT, UPDATE, DELETE
AS
BEGIN
    if exists(select * from inserted)
    -- we're covering just insert cases here..
    begin
       insert into my_table(col1, col2, col3, ..., col_timestamp)
       select inserted.col1, inserted.col2...., CURRENT_TIMESTAMP from inserted
    end
END

GO