In the "Your own adventure" books, the reader starts at page 1, and every page either (1) ends the story, or (2) sends him to another page, or (3) offers a choice among two possible pages.

Knowing that:

each page can be reached from only one other page -- except for the 1st page, that cannot be reached from any page;
that all pages can eventually be reached by picking an appropriate path from page 1;
that if a book can be converted into another just by reordering choices and renumbering pages, they are considered to be the same;and that these books are always 100 pages long...How many essentially different books can be published?

(In reply to

re: Program needed . . . by Charlie)

An objection... when we have 2n nodes, and we add 1, if we add F(n)*F(n) to the sum, we will have repeated some combinations.

Call the F(n) different books A, B, C, ...Z. We could have A with any of A to Z, but B only with B to Z (A with B has been done), and C only with C to Z... and so on, so in this case we should add F(n)*(F(n)+1)/2.