|
Search: id:A114997
|
|
|
| A114997 |
|
Number of ordered trees with n edges and no unary or binary nodes. |
|
+0
1
|
|
| 1, 1, 1, 4, 8, 13, 31, 71, 144, 318, 729, 1611, 3604, 8249, 18803, 42907, 98858, 228474, 528735, 1228800, 2865180, 6693712, 15676941, 36807239, 86584783, 204060509, 481823778, 1139565120
(list; graph; listen)
|
|
|
OFFSET
|
3,4
|
|
|
COMMENT
|
Also counts sequences of n natural numbers, excluding 1 and 2, such that the sum of every prefix is no more than its length.
|
|
LINKS
|
Nachum Dershowitz and Shmuel Zaks, Up and Down, Young and Old, Odd and Even, draft.
|
|
FORMULA
|
a(n) = Sum_{(n+3)/2 <= k <= n} (1/(n+1) binomial(n+1, k) binomial(2k-n-3, n-k))
|
|
CROSSREFS
|
Cf. A005043.
Adjacent sequences: A114994 A114995 A114996 this_sequence A114998 A114999 A115000
Sequence in context: A080003 A033016 A027008 this_sequence A138634 A125495 A114971
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Nachum Dershowitz (Nachumd(AT)tau.ac.il), Feb 23 2006
|
|
|
Search completed in 0.002 seconds
|
