A355671 Number of labeled trees on [n] that are bicentered.

0, 0, 1, 0, 12, 60, 570, 8190, 134456, 2408616, 49307670, 1159112130, 30619757652, 891045909468, 28244653953698, 969331283419590, 35858099428919280, 1423688804991442896, 60402176709135347502, 2726896792761748601226, 130498364319404393167820

Offset

0,5

Comments

This is the labeled version of A000677 where pertinent definitions can be found.

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_{odd d} A034854(n,d).

a(n) = A000272(n) - A356292(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[H[m, z]^2/2, {z, 0, nn}], z], {m, 1, nn/2 - 1}], 3 -> 1]

Crossrefs

Cf. A034854, A000677, A356292, A000272.

Sequence in context: A012706 A012359 A012707 * A108096 A056388 A056378

Adjacent sequences: A355668 A355669 A355670 * A355672 A355673 A355674

Keyword

nonn

Author

Geoffrey Critzer, Aug 02 2022

Status

approved