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A292555 Number of rooted unlabeled trees on n nodes where each node has at most 10 children. 11
1, 1, 1, 2, 4, 9, 20, 48, 115, 286, 719, 1842, 4765, 12483, 32964, 87785, 235305, 634628, 1720524, 4686842, 12820920, 35206475, 97010705, 268154003, 743351390, 2066090876, 5756490561, 16074597300, 44980514021, 126109353817, 354202275766, 996517941454 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
Functional equation of G.f. is T(z) = z + z*Sum_{q=1..10} 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_10)(T(z)).
a(n) = Sum_{j=1..10} A244372(n,j) for n>0, a(0) = 1. - Alois P. Heinz, Sep 20 2017
a(n) / a(n+1) ~ 0.338329194566131211670667671160855741193081902868090986608524... - Robert A. Russell, Feb 11 2023
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, 10$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, 10, 10]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jun 04 2018, after Alois P. Heinz *)
CROSSREFS
Column k=10 of A299038.
Sequence in context: A255640 A216403 A145548 * A318804 A318857 A145549
KEYWORD
nonn
AUTHOR
Marko Riedel, Sep 18 2017
STATUS
approved

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)