I'm assuming Francis and Frank are the same person; they may not be.

1.  Marriage Record:

2.  1800

3.  1810

4.  1820
Henry "MARCHEN" is in the 1820 census of Caldwell Co., KY, and is the only MACHEN, or variation, in Caldwell Co.

5.  1830

6.  1840

7.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  District No. 1, Caldwell Co., KY, p. 312B, 488/488, enumerated 30 Aug 1850 (extracted by Diana Gale Matthiesen):

Henry Machen	74	M	Farmer	6000	Virginia
Nancy   "	77	F			"
Ellen M. Cobb	14	F			Caldwell cty Ky

Living next door to son, Francis MACHEN (æ 32, b. Caldwell Co., KY).

8.  J.H. Battle, W.H. Perrin, & G.C. Kniffin.  1887. Kentucky, a History of the State.  F.A. Battey & Co., Louisville, KY (excerpts online at the Kentucky Biographies Project [link died]):

EX-UNITED STATES SENATOR, WILLIS B. MACHEN was born April 5, 1810 in Caldwell, now Lyon County, Ky.  His parents, Henry and Nancy (Tarrant) Machen, came from South Carolina in 1809, located on a farm near where subject now resides.  The father was a prosperous farmer, and a man of much energy and good sense.  His death occurred in 1860; that of his wife in 1852.  There are only two of their children living - subject, and Frank, of Princeton, Ky.  The Machens are the out-growth of intermarriages on one side of Huguenots and Irish, and Scotch and English on the other.  Many of the ancestral connection [sic], of Mr. Machen served the colonies with distinction during the war of Independence, among others was his great- grandfather Woods, who was killed by the Tories, and whose death was severely avenged by his brother, Col. Woods, of South Carolina...

9.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).

10.  Terry Reigel.  Reigel Roots. [link died]