|
| |
|
|
A356292
|
|
Number of labeled trees on [n] that are centered.
|
|
2
|
|
|
|
1, 1, 0, 3, 4, 65, 726, 8617, 127688, 2374353, 50692330, 1198835561, 31297606572, 901114484569, 28449258421598, 976863784939785, 36199494609008656, 1438734246518372897, 61037354387458904274, 2753490065023053584713, 131645635680595606832180
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,4
|
|
|
COMMENTS
|
This is the labeled version of A000676 which has the pertinent definitions.
|
|
|
LINKS
|
Table of n, a(n) for n=0..20.
J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
Index entries for sequences related to trees
|
|
|
FORMULA
|
a(n) = Sum_{d even} A034854(n,d).
a(n) = A000272(n) - A355671(n)
|
|
|
MATHEMATICA
|
nn = 20; T = NestList[z Exp[#] &, z, nn]; G[k_, z_] := T[[k + 1]]; H[k_, z_] := T[[k + 1]] - T[[k]]; H[0, z_] := z; ReplacePart[ Sum[Range[0, nn]!CoefficientList[Series[G[m, z] (Exp[H[m, z]] - 1 - H[m, z]), {z, 0, nn}], z], {m, 0, nn/2 - 2}], {1 -> 1, 2 -> 1}]
|
|
|
CROSSREFS
|
Cf. A034854, A000676, A000272, A355671.
Sequence in context: A274699 A060356 A052323 * A012087 A012194 A318208
Adjacent sequences: A356289 A356290 A356291 * A356293 A356294 A356295
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Geoffrey Critzer, Aug 02 2022
|
|
|
STATUS
|
approved
|
| |
|
|
