Since no-one has tried to answer this question, I'll do a rough back-of-the-envelope estimate...

How many cells are in a newborn?

One estimate puts the number of human cells in a 70kg male at 37 trillion cells, or 37x10

^{12}.

See Dr Karl's summary:

http://www.abc.net.au/science/articles/2015/11/10/4346790.htmAssuming that individual adult cells are roughly similar mass to the cells in a newborn, the number of cells in a 4kg newborn is this number times 4/70, or 2x10

^{12} cells.

This ignores the huge number of commensual bacteria which live in adults (and it seems, a smaller number which have already colonized a newborn).

How many times must a fertilized ovum divide to form a normal term baby?

The

*minimum* number of divisions to reach this number is LOG

_{2}(2x10

^{12}) = LOG

_{10}(2x10

^{12})/LOG

_{10}(2) ≈ 41 divisions.

This does

*not* account for apoptosis, which will require additional divisions to produce the cells which subsequently die.

Does this account for the placenta?

Part of the placenta forms from the fertilized egg, and part grows from the mother's tissue. So it

*partly* includes the placenta.

The placenta functions as a fetomaternal organ with two components: the fetal placenta (Chorion frondosum), which develops from the same blastocyst that forms the fetus, and the maternal placenta (Decidua basalis), which develops from the maternal uterine tissue

How fast is the cell division curve in each month?

41 divisions in 9 months averages out at 0.9 per week (or a bit faster, if you account for apotosis).

A blastocyst at 6 days after fertilization has 200-300 cells; this represents about 8 divisions.

So in the first week, divisions happen more than once per day.

See:

https://en.wikipedia.org/wiki/Blastocyst