read `Compositions.txt`:


R:=10:
print(`Generating functions for Enumerating Compositions of Depth Less than r, for r from 1 to`, R):
print(``):
print(`By Shalosh B. Ekhad`):
print(``):
print(`In the article "The Depth of Compositions" by  A. Blecher, C. Brennan, A. Knopfmacher and T. Mansour` ):
print(`To appear in "Mathematics in Computer Science", it is proved (Prop. 1) that a composition is of depth`):
print(` STRICTLY less than r, iff, it AVOIDS the composition`):
print(`r(r+1) ...(2r-2)(2r-1)(2r-2)...r `):
print(`Using procedure GFone(C,x), in the Maple package Compositions.txt, we can compute the enumerating generating functions for`):
print(`for any given r. We will do it for r up to`, R):

for r from 1 to R do
print(`Theorem Number:`, r, `The generating function enumerating compositions of depth STRICTLY less than`, r, `is given as follows.`):
print(``):
InfoV({Taur(r)},x,40):
print(``):
od:

print(``):
print(`---------------------------------`):
print(``):

print(`This took`, time(), `seconds. `):

quit: