Lah Number - Rising and Falling Factorials

Rising and Falling Factorials

Let represent the rising factorial and let represent the falling factorial .

Then and

For example,

Compare the third row of the table of values.

Read more about this topic:  Lah Number

Famous quotes containing the words rising and, rising and/or falling:

    Over the tree-tops I float thee a song,
    Over the rising and sinking waves, over the myriad fields and the
    prairies wide,
    Over the dense-packed cities all and the teeming wharves and ways,
    I float this carol with joy, with joy to thee, O death,
    Walt Whitman (1819–1892)

    Consider the difference between looking and staring. A look is voluntary; it is also mobile, rising and falling in intensity as its foci of interest are taken up and then exhausted. A stare has, essentially, the character of a compulsion; it is steady, unmodulated, “fixed.”
    Susan Sontag (b. 1933)

    I can never suppose this country so far lost to all ideas of self-importance as to be willing to grant America independence; if that could ever be adopted I shall despair of this country being ever preserved from a state of inferiority and consequently falling into a very low class among the European States.
    George III (1738–1820)