|
Search: id:A062994
|
|
|
| A062994 |
|
Eighth column of triangle A062993 (without leading zeros). A Pfaff-Fuss or 9-Raney sequence. |
|
+0
7
|
|
| 1, 1, 9, 117, 1785, 29799, 527085, 9706503, 184138713, 3573805950, 70625252863, 1416298046436, 28748759731965, 589546754316126, 12195537924351375, 254184908607118800, 5332692942907262361
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
See Graham et al., Hilton and Pedersen, Hoggat and Bicknell, Frey and Sellers references given in A062993.
a(n), n>=1, enumerates 9-ary trees (rooted, ordered, incomplete) with n vertices (including the root). See A059967.
|
|
REFERENCES
|
G. P\'olya and G. Szeg\"o, Problems and Theorems in Analysis, Springer-Verlag, Heidelberg, New York, 2 vols., 1972, Vol. 1, problem. 211, p. 146 with solution on p. 348.
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=0,...,100
|
|
FORMULA
|
a(n)= A062993(n+9, 9)= binomial(9*n, n)/(8*n+1).
G.f.: RootOf((_Z^9)*x-_Z+1) (Maple notation, from ECS, see links for A007556).
|
|
EXAMPLE
|
There are a(2)=9 9-ary trees (vertex degree <=9 and 9 possible branchings) with 2 vertices (one of them the root). Adding one more branch (one more vertex) to these 9 trees yields 9*9+binomial(9,2)=117=a(3) such trees.
|
|
PROGRAM
|
(PARI) { for (n=0, 100, write("b062994.txt", n, " ", binomial(9*n, n)/(8*n + 1)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Aug 15 2009]
|
|
CROSSREFS
|
A000108, A001764, A002293-6, A007556, A062744.
Sequence in context: A092913 A022607 A139740 this_sequence A059967 A027396 A113344
Adjacent sequences: A062991 A062992 A062993 this_sequence A062995 A062996 A062997
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 12 2001
|
|
EXTENSIONS
|
9-ary tree comments and P\'olya and G. Szeg\"o reference by W. Lang, Sep 14 2007.
|
|
|
Search completed in 0.002 seconds
|
