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A000342
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Number of n-node rooted trees of height 5.
(Formerly M3884 N1594)
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2
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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)
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OFFSET
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1,7
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REFERENCES
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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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LINKS
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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
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FORMULA
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A001385-A001384. (Christian G. Bower).
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MAPLE
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For Maple program see link in A000235.
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MATHEMATICA
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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 *)
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CROSSREFS
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Column h=5 of A034781.
Sequence in context: A102841 A036637 A036644 * A189427 A355492 A212339
Adjacent sequences: A000339 A000340 A000341 * A000343 A000344 A000345
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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