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 A303259 Number of ordered rooted trees with n non-root nodes such that the maximal outdegree equals ceiling(n/2). 3
 1, 1, 1, 3, 8, 15, 53, 84, 326, 495, 1997, 3003, 12370, 18564, 77513, 116280, 490306, 735471, 3124541, 4686825, 20030000, 30045015, 129024469, 193536720, 834451788, 1251677700, 5414950283, 8122425444, 35240152706, 52860229080, 229911617041, 344867425584 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2417 FORMULA a(n) = A203717(n,ceiling(n/2)). MAPLE b:= proc(u, o, k) option remember; `if`(u+o=0, 1, add(b(u-j, o+j-1, k), j=1..min(1, u))+ add(b(u+j-1, o-j, k), j=1..min(k, o))) end: a:= n-> `if`(n=0, 1, (j-> b(0, n, j)-b(0, n, j-1))(ceil(n/2))): seq(a(n), n=0..35); 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_] := If[n == 0, 1, With[{j = Ceiling[n/2]}, b[0, n, j]-b[0, n, j-1]]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Mar 19 2022, after Alois P. Heinz *) CROSSREFS Bisections give: A291662 (even part), A005809 (odd part). Cf. A203717. Sequence in context: A032064 A151397 A216466 * A192167 A065500 A120341 Adjacent sequences: A303256 A303257 A303258 * A303260 A303261 A303262 KEYWORD nonn AUTHOR Alois P. Heinz, Apr 20 2018 STATUS approved

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Last modified June 10 20:26 EDT 2023. Contains 363207 sequences. (Running on oeis4.)