|
| |
|
|
A000524
|
|
Number of rooted trees with n nodes, 2 of which are labeled.
(Formerly M1927 N0761)
|
|
11
| |
|
|
2, 9, 34, 119, 401, 1316, 4247, 13532, 42712, 133816, 416770, 1291731, 3987444, 12266845, 37627230, 115125955, 351467506, 1070908135, 3257389088, 9892759091, 30002923380, 90879555521, 274963755791, 831064788976
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,1
|
|
|
REFERENCES
| J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 134.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=2..200
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
|
|
|
FORMULA
| G.f.: A(x) = B(x)^3+2*B(x)^2 where B(x) is g.f. of A000107.
G.f.: A(x) = B(x)^2*(2-B(x))/(1-B(x))^3, where B(x) is g.f. for rooted trees with n nodes, cf. A000081. - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 19 2001
|
|
|
MAPLE
| b:= proc(n) option remember; if n<=1 then n else add(k*b(k)* s(n-1, k), k=1..n-1)/(n-1) fi end: s:= proc(n, k) option remember; add(b(n+1-j*k), j=1..iquo(n, k)) end: B:= proc(n) option remember; add (b(k)*x^k, k=1..n) end: a:= n-> coeff (series (B(n-1)^2*(2-B(n-1))/(1-B(n-1))^3, x=0, n+1), x, n): seq (a(n), n=2..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 21 2008]
|
|
|
CROSSREFS
| Cf. A000081, A000107, A000243, A000269, A000444, A000485, A000525, A000526.
Sequence in context: A150935 A150936 A109719 * A120989 A010763 A077234
Adjacent sequences: A000521 A000522 A000523 * A000525 A000526 A000527
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms, new description and formula from Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
|
| |
|
|
