login
The OEIS is supported by
the many generous donors to the OEIS Foundation
.
Hints
(Greetings from
The On-Line Encyclopedia of Integer Sequences
!)
A038057
a(n) = 2^n*n^(n-1).
4
2, 8, 72, 1024, 20000, 497664, 15059072, 536870912, 22039921152, 1024000000000, 53119845582848, 3043362286338048, 190857913323364352, 13004222844995895296, 956593800000000000000, 75557863725914323419136
(
list
;
graph
;
refs
;
listen
;
history
;
text
;
internal format
)
OFFSET
1,1
COMMENTS
Labeled rooted trees with n 2-colored nodes.
LINKS
Table of n, a(n) for n=1..16.
Index entries for sequences related to rooted trees
FORMULA
E.g.f.: B(2*x) where B(x) is e.g.f. of
A000169
.
Limit_{n->oo} a(n+1)/(n*a(n)) = 2*e. -
Stefano Spezia
, Mar 12 2023
MATHEMATICA
nn=16; f[x_]:=Sum[a[n]x^n/n!, {n, 0, nn}]; s=SolveAlways[0==Series[f[x]-2x Exp[f[x]], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}]/.s
(* or *)
nn=16; Drop[Range[0, nn]!CoefficientList[Series[-LambertW[-2x], {x, 0, nn}], x], 1]
(* or *)
Table[2^n*n^(n-1), {n, 1, 16}] (*
Geoffrey Critzer
, Mar 17 2013 *)
CROSSREFS
Cf.
A000169
,
A019762
(2*e),
A038055
-
A038062
.
Equals 2 *
A052746
(n).
Sequence in context:
A364408
A194499
A009478
*
A107270
A294351
A342177
Adjacent sequences:
A038054
A038055
A038056
*
A038058
A038059
A038060
KEYWORD
nonn
AUTHOR
Christian G. Bower
, Jan 04 1999
EXTENSIONS
New description from
Vladeta Jovovic
, Mar 08 2003
STATUS
approved
Lookup
|
Welcome
|
Wiki
|
Register
|
Music
|
Plot 2
|
Demos
|
Index
|
Browse
|
More
|
WebCam
Contribute new seq. or comment
|
Format
|
Style Sheet
|
Transforms
|
Superseeker
|
Recents
The OEIS Community
| Maintained by
The OEIS Foundation Inc.
License Agreements, Terms of Use, Privacy Policy.
.
Last modified April 17 13:58 EDT 2024. Contains 371764 sequences. (Running on oeis4.)