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

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Last modified January 30 21:42 EST 2023. Contains 359947 sequences. (Running on oeis4.)