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 A000235 Number of n-node rooted trees of height 3. (Formerly M2732 N1097) 16
 0, 0, 0, 1, 3, 8, 18, 38, 76, 147, 277, 509, 924, 1648, 2912, 5088, 8823, 15170, 25935, 44042, 74427, 125112, 209411, 348960, 579326, 958077, 1579098, 2593903, 4247768, 6935070, 11290627, 18330973, 29684082, 47946852, 77258764, 124198083 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS (1, 1, 2, 3, 5, 8, ...) convolved with (0, 0, 1, 2, 4, 7, ...) = (0, 0, 1, 3, 8, ...). - Gary W. Adamson, Aug 14 2010 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. N. J. A. Sloane, Maple programs for counting rooted trees by height (after Riordan) FORMULA a(n) = A001383(n) - A000041(n-1). - Christian G. Bower MAPLE # For Maple program see link. with(combstruct): ZL:= proc(m) local i; [T0, {seq(T||i=Prod(Z, Set(T||(i+1))), i=0..m-1), T||m=Z}, unlabeled] end: A000235:= n-> count(ZL(3), size=n)-count(ZL(2), size=n): seq(A000235(n), n=1..36); # Zerinvary Lajos, Sep 23 2007 MATHEMATICA m = 36; Rest @ CoefficientList[ Series[x*Product[(1-x^k)^(-PartitionsP[k-1]), {k, 1, m}], {x, 0, m}], x] - PartitionsP[Range[0, m-1]] (* Jean-François Alcover, Jul 05 2011, after Christian G. Bower *) CROSSREFS Column h=3 of A034781. Sequence in context: A261446 A078409 A036642 * A006478 A104187 A051633 Adjacent sequences:  A000232 A000233 A000234 * A000236 A000237 A000238 KEYWORD nonn AUTHOR STATUS approved

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