The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A291823 Number of ordered rooted trees with n non-root nodes and all outdegrees <= eight. 3
 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4861, 16785, 58708, 207557, 740520, 2662812, 9640581, 35112513, 128563215, 472951884, 1747233370, 6479450415, 24111470952, 90006390290, 336953657070, 1264770431964, 4758911027946, 17946417454046, 67818937355227, 256781370248500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Also the number of Dyck paths of semilength n with all ascent lengths <= eight. Also the number of permutations p of [n] such that in 0p all up-jumps are <= eight and no down-jump is larger than 1. An up-jump j occurs at position i in p if p_{i} > p_{i-1} and j is the index of p_i in the increasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are larger than p_{i-1}. A down-jump j occurs at position i in p if p_{i} < p_{i-1} and j is the index of p_i in the decreasingly sorted list of those elements in {p_{i}, ..., p_{n}} that are smaller than p_{i-1}. First index in the lists is 1 here. Differs from A000108 first at n = 9. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 N. Hein and J. Huang, Modular Catalan Numbers, arXiv:1508.01688 [math.CO], 2015 Index entries for sequences related to rooted trees FORMULA G.f.: G(x)/x where G(x) is the reversion of x*(1-x)/(1-x^9). - Andrew Howroyd, Nov 30 2017 G.f. A(x) satisfies: A(x) = 1 + Sum_{k=1..8} x^k*A(x)^k. - Ilya Gutkovskiy, May 03 2019 MAPLE b:= proc(u, o) option remember; `if`(u+o=0, 1, add(b(u-j, o+j-1), j=1..min(1, u))+ add(b(u+j-1, o-j), j=1..min(8, o))) end: a:= n-> b(0, n): seq(a(n), n=0..30); MATHEMATICA b[u_, o_, k_] := b[u, o, k] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1, k], {j, 1, Min[1, u]}] + Sum[b[u + j - 1, o - j, k], {j, 1, Min[k, o]}]]; a[n_] := b[0, n, 8]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 07 2017, after Alois P. Heinz *) PROG (PARI) Vec(serreverse(x*(1-x)/(1-x*x^8) + O(x*x^25))) \\ Andrew Howroyd, Nov 29 2017 CROSSREFS Column k=8 of A288942. Cf. A000108. Sequence in context: A287971 A033191 A261591 * A287972 A243838 A242450 Adjacent sequences: A291820 A291821 A291822 * A291824 A291825 A291826 KEYWORD nonn AUTHOR Alois P. Heinz, Sep 01 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 09:31 EST 2023. Contains 367710 sequences. (Running on oeis4.)