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 A000342 Number of n-node rooted trees of height 5. (Formerly M3884 N1594) 2
 0, 0, 0, 0, 0, 1, 5, 19, 61, 180, 498, 1323, 3405, 8557, 21103, 51248, 122898, 291579, 685562, 1599209, 3705122, 8532309, 19543867, 44552066, 101124867, 228640542, 515125815, 1156829459, 2590247002, 5784031485, 12883390590, 28629914457 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 REFERENCES 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). LINKS N. J. A. Sloane, Table of n, a(n) for n=1..200 J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478. 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 rooted trees Index entries for sequences related to trees FORMULA A001385-A001384. (Christian G. Bower). MAPLE For Maple program see link in A000235. MATHEMATICA f[n_] := Nest[CoefficientList[Series[Product[1/(1 - x^i)^#[[i]], {i, 1, Length[#]}], {x, 0, 40}], x] &, {1}, n]; f[5]-f[4] (* Geoffrey Critzer, Aug 01 2013 *) b[n_, i_, k_] := b[n, i, k] = If[n==0, 1, If[i<1 || k<1, 0, Sum[ Binomial[ b[i-1, i-1, k-1]+j-1, j]*b[n-i*j, i-1, k], {j, 0, n/i}]]]; a[n_] := b[n- 1, n-1, 5] - b[n-1, n-1, 4]; Array[a, 40] (* Jean-François Alcover, Feb 07 2016, after Alois P. Heinz in A034781 *) CROSSREFS Column h=5 of A034781. Sequence in context: A102841 A036637 A036644 * A189427 A355492 A212339 Adjacent sequences: A000339 A000340 A000341 * A000343 A000344 A000345 KEYWORD nonn AUTHOR N. J. A. Sloane STATUS approved

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)