0,4

This is the labeled version of A000676 which has the pertinent definitions.

J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)

a(n) = Sum_{d even} A034854(n,d).

a(n) = A000272(n) - A355671(n)

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}]

Cf. A034854, A000676, A000272, A355671.

Sequence in context: A274699 A060356 A052323 * A012087 A012194 A318208

Adjacent sequences: A356289 A356290 A356291 * A356293 A356294 A356295

Geoffrey Critzer, Aug 02 2022

approved