A355671
Number of labeled trees on [n] that are bicentered.
Original entry on oeis.org
0, 0, 1, 0, 12, 60, 570, 8190, 134456, 2408616, 49307670, 1159112130, 30619757652, 891045909468, 28244653953698, 969331283419590, 35858099428919280, 1423688804991442896, 60402176709135347502, 2726896792761748601226, 130498364319404393167820
Offset: 0
-
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]
A356292
Number of labeled trees on [n] that are centered.
Original entry on oeis.org
1, 1, 0, 3, 4, 65, 726, 8617, 127688, 2374353, 50692330, 1198835561, 31297606572, 901114484569, 28449258421598, 976863784939785, 36199494609008656, 1438734246518372897, 61037354387458904274, 2753490065023053584713, 131645635680595606832180
Offset: 0
-
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}]
A001852
Total diameter of labeled trees with n nodes.
Original entry on oeis.org
0, 1, 6, 44, 430, 5322, 79184, 1381144, 27730602, 630422390, 16006336852, 448982630340, 13792542282974, 460632431511826, 16620059192605080, 644338908974954672, 26713929408696716242, 1179487563859389821166
Offset: 1
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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