Word Chain (?) Bird to Nest

Lloyd is quite fond of math, and likes to incorporate math into almost everything he does. One weekend, the local newspaper printed a Word Chain puzzle, with starting point BIRD and ending with NEST. I had some trouble solving it, and asked Lloyd for help. He told me that he had solved it, and handed me his copy of the puzzle.

When I looked at Lloyd’s “solution”, I didn’t see a chain of words, just a sequence of math operations. Seeing as this is Lloyd, I figured that it really was a solution, but I couldn’t figure out what he was doing.

Here is Lloyd’s solution. Can you reconstruct the actual word chain?

BIRD
     -  5408
     +    15
     + 17576
     +     1
     +    26
     +158184
     +  2704
NEST + 35152