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A034855
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Triangle read by rows giving number of rooted labeled trees with n >= 2 nodes and height d >= 1.
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7
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2, 3, 6, 4, 36, 24, 5, 200, 300, 120, 6, 1170, 3360, 2520, 720, 7, 7392, 38850, 43680, 22680, 5040, 8, 50568, 475776, 757680, 551040, 221760, 40320, 9, 372528, 6231960, 13747104, 12836880, 7136640, 2358720, 362880, 10, 2936070, 87530400, 264181680
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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LINKS
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Alois P. Heinz, Rows n = 2..101, flattened
J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
Index entries for sequences related to trees
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FORMULA
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Reference gives recurrence.
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EXAMPLE
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2;
3, 6;
4, 36, 24;
5, 200, 300, 120;
6, 1170, 3360, 2520, 720;
7, 7392, 38850, 43680, 22680, 5040;
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MAPLE
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gf:= proc(k) gf(k):= `if`(k=0, x, x*exp(gf(k-1))) end:
A:= proc(n, k) A(n, k):= n!*coeff(series(gf(k), x, n+1), x, n) end:
T:= (n, d)-> A(n, d) -A(n, d-1):
seq(seq(T(n, d), d=1..n-1), n=2..12); # Alois P. Heinz, Sep 21 2012
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MATHEMATICA
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gf[k_] := gf[k] = If[k == 0, x, x*E^gf[k - 1]]; a[n_, k_] := n!*Coefficient[ Series[gf[k], {x, 0, n + 1}], x, n]; t[n_, d_] := a[n, d] - a[n, d - 1]; Table[t[n, d], {n, 2, 12}, {d, 1, n - 1}] // Flatten (* Jean-François Alcover, Jan 15 2013, translated from Alois P. Heinz's Maple program *)
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CROSSREFS
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Cf. A001854, A234953, A000435, A236396.
Sequence in context: A096357 A091507 A098282 * A105214 A136315 A011159
Adjacent sequences: A034852 A034853 A034854 * A034856 A034857 A034858
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004
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STATUS
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approved
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