Here is my best attempt to count the approximate number of cells at each stage:
Zygote (fertilized egg): 1 cell
2-cell stage: 2 cells
4-cell stage: 4 cells
8-cell stage: 8 cells
16-cell stage: 16 cells
32-cell stage: 32 cells
64-cell stage: 64 cells
Morula: 128 cells
Blastocyst: 150 cells
Gastrula: 1,000 cells
Neurula: 10,000 cells
Early organogenesis: 100,000 cells
Fetus: 1 trillion cells
Newborn baby: 10 trillion cells
Adult: 30-40 trillion cells