LOS ANGELES — Barry Manilow has told the story behind his first big hit so many times that I had no intention of bringing up the half-century-old “Mandy” when I sat down with the singer on a recent afternoon at his home in Palm Springs. Among the questions I did ask was how he ended up recording the song that opens his new album, and the answer — as it’s so often been throughout Manilow’s career, beginning with that 1975 chart-topper — was Clive…