A356292 Number of labeled trees on [n] that are centered.

1, 1, 0, 3, 4, 65, 726, 8617, 127688, 2374353, 50692330, 1198835561, 31297606572, 901114484569, 28449258421598, 976863784939785, 36199494609008656, 1438734246518372897, 61037354387458904274, 2753490065023053584713, 131645635680595606832180

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