Elizabeth is rather young to have birthed Charles in 1815 — we may have Charles's age wrong and/or Elizabeth may have be fibbing about her age in the 1850 census.

— born in Jefferson Co., MO:
  8.  Elizabeth HENDRICKSON, b. ca. 1831
  9.  Caroline HENDRICKSON, b. ca. 1834
10.  Mary Ann HENDRICKSON, b. 1834/5
11.  Richard HENDRICKSON, b. ca. 1836

1.  Jordan R. Dodd, ed.  1993.  Missouri Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-227):

Hendrickson, John	Lucas, Baliza	25 Dec 1829	Jefferson Co.
Burton, Thomas	Hendrickson, Elizabeth	14 May 1838	Jefferson Co.
Henrickson, Richard	Crow, Eleanor	16 Apr 1840	Jefferson Co.
Peppers, Joseph	Hendrickson, Eliza	8 Aug 1841	Jefferson Co.
Hendrickson, William	Ogle, Sophia	27 Jan 1848	Jefferson Co.

2.  Census Index:  U.S. Selected Counties, 1820 (Broderbund CD-314):  not found, but there was no 1820 Federal Census in Missouri because it had not yet become a state.

3.  1830 Census Index/Images (online at Ancestry.com; Image #5 of 12 — mis-indexed "Kendreckson"; extracted by Diana Gale Matthiesen):

1830

MO

Jefferson Co.

Joachim Twp.

p. 121

Ln. 18

Richard Hendrickson

212 001 - 110 010

no slaves

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	4 or under	1825-1830	=
1 male	5-9	1820-1825	=
2 males	10-14	1815-1820	=
1 male	30-39	1790-1800	= Richard
1 female	4 or under	1825-1830	=
1 female	5-9	1820-1825	=
1 female	20-29	1800-1810	= Elizabeth (b. 1799/1800)

Listed three lines from Jonathan HENDRICKSON (1110001001-101001), whose age (70-80) makes it likely he is Richard's father.

4.  1840 Census Index/Images (online at Ancestry.com, Image #0-1 of 9 — missing from the index; numerical data pages precede the name pages; extracted by Diana Gale Matthiesen):

1840

MO

Jefferson Co.

Valleé Twp.

pp. 112A-112B

Ln. 20

Richard Hendrickson

112 200 100 - 031 100 100

0200000

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	4 or under	1835-1840	=
1 male	5-9	1830-1835	=
2 males	10-14	1825-1830	=
2 males	15-19	1820-1825	=
1 male	40-49	1790-1800	= Richard
3 females	5-9	1830-1835	= Mary Ann (b. 1834/5)
1 female	10-14	1825-1830	=
1 female	15-19	1820-1825	=
1 female	40-49	1790-1800	= Elizabeth (b. 1799/1800)
2	persons employed in agriculture

5.  1850 Census Index/Images (online at Ancestry.com; Image #141 of 153):  District No. 42, Jefferson Co., MO, p. 477A, 1059/1059, enumerated 30 Oct 1850, official enumeration date 1 Jun 1850 (extracted by Diana Gale Matthiesen):¤•

Peter Stroup	63	M		Farmer	700	NC
Elizabeth "	50	F				Ky
William   "	20	M		Farmer		Mo
Clarrissa "	18	F				Mo
Richard   "	12	M				Mo
Peter     "	10	M				Mo
John      "	6	M				Mo
Mary A Hendrickson	15	F				Mo

Widow Elizabeth has remarried.