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 A000429 Number of n-node rooted trees of height 8. (Formerly M4525 N1918) 2
 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 43, 188, 728, 2593, 8706, 27961, 86802, 262348, 776126, 2256418, 6466614, 18311915, 51334232, 142673720, 393611872, 1078955836, 2941029334, 7977065816, 21541492856, 57942770689, 155304829763, 414934057486 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 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. FORMULA a(n) = A034825(n) - A034824(n). - Christian G. Bower MAPLE For Maple program see link in A000235. MATHEMATICA 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, 8] - b[n - 1, n - 1, 7]; Array[a, 40] (* Jean-François Alcover, Feb 08 2016, after Alois P. Heinz in A034781 *) CROSSREFS Column h=8 of A034781. Sequence in context: A036633 A036640 A036647 * A055853 A137748 A005024 Adjacent sequences: A000426 A000427 A000428 * A000430 A000431 A000432 KEYWORD nonn AUTHOR STATUS approved

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Last modified March 31 14:43 EDT 2023. Contains 361663 sequences. (Running on oeis4.)