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 A292556 Number of rooted unlabeled trees on n nodes where each node has at most 11 children. 11
 1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4766, 12485, 32970, 87802, 235355, 634771, 1720940, 4688041, 12824394, 35216524, 97039824, 268238379, 743596131, 2066801045, 5758552717, 16080588286, 44997928902, 126160000878, 354349643101, 996946927831 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Marko Riedel, Trees with bounded degree. FORMULA Functional equation of G.f. is T(z) = z + z*Sum_{q=1..11} Z(S_q)(T(z)) with Z(S_q) the cycle index of the symmetric group. Alternate FEQ is T(z) = 1 + z*Z(S_11)(T(z)). a(n) = Sum_{j=1..11} A244372(n,j) for n>0, a(0) = 1. - Alois P. Heinz, Sep 20 2017 MAPLE b:= proc(n, i, t, k) option remember; `if`(n=0, 1,       `if`(i<1, 0, add(binomial(b((i-1)\$2, k\$2)+j-1, j)*        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))     end: a:= n-> `if`(n=0, 1, b(n-1\$2, 11\$2)): seq(a(n), n=0..35);  # Alois P. Heinz, Sep 20 2017 MATHEMATICA b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[ b[i-1, i-1, k, k]+j-1, j]*b[n-i*j, i-1, t-j, k], {j, 0, Min[t, n/i]}]]]; a[n_] := If[n == 0, 1, b[n-1, n-1, 11, 11]]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 05 2018, after Alois P. Heinz *) CROSSREFS Cf. A000081, A001190, A000598, A036718, A036721, A036722, A182378, A244372, A292553, A292554, A292555. Column k=11 of A299038. Sequence in context: A318804 A318857 A145549 * A145550 A000081 A123467 Adjacent sequences:  A292553 A292554 A292555 * A292557 A292558 A292559 KEYWORD nonn AUTHOR Marko Riedel, Sep 18 2017 STATUS approved

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Last modified December 12 03:27 EST 2018. Contains 318052 sequences. (Running on oeis4.)