|
Search: id:A027852
|
|
|
| A027852 |
|
Number of connected functions on n points with a loop of length 2. |
|
+0
2
|
|
| 0, 1, 1, 3, 6, 16, 37, 96, 239, 622, 1607, 4235, 11185, 29862, 80070, 216176, 586218, 1597578, 4370721, 12003882, 33077327, 91433267, 253454781, 704429853, 1962537755, 5479855546, 15332668869, 42983656210
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
Also rooted trees on n+1 nodes where root has degree 2.
|
|
LINKS
|
Index entries for sequences related to rooted trees
|
|
FORMULA
|
G.f.: A(x) = (B(x)^2 + B(x^2))/2 where B(x) is g.f. of A000081.
|
|
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; unapply (add (b(k)*x^k, k=1..n), x) end: a:= n-> coeff (series ((B(n-1)(x)^2 +B(n-1)(x^2))/2, x=0, n+1), x, n): seq (a(n), n=1..28); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
|
|
CROSSREFS
|
Cf. A000081, A000226, A001372, A002861.
Sequence in context: A130095 A072824 A089406 this_sequence A114410 A096588 A073079
Adjacent sequences: A027849 A027850 A027851 this_sequence A027853 A027854 A027855
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Christian G. Bower (bowerc(AT)usa.net), Dec 14 1997
|
|
EXTENSIONS
|
Edited by Christian G. Bower (bowerc(AT)usa.net), Feb 12 2002
|
|
|
Search completed in 0.002 seconds
|
