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 falling, rising and, rising and/or falling:

    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)

    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)

    Removed from its more restrictive sense, masturbation has become an expression for everything that has proved, for lack of human contact, to be void of meaning. We have communication problems, suffer from egocentrism and narcissism, are frustrated by information glut and loss of environment; we stagnate despite the rising GNP.
    Günther Grass (b. 1927)

    We saw the lightning and that was the guns; and then we heard the thunder and that was the big guns; and then we heard the rain falling and that was the blood falling; and when we came to get in the crops, it was dead men that we reaped.
    Harriet Tubman (1821–1913)