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A292556
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Number of rooted unlabeled trees on n nodes where each node has at most 11 children.
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12
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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
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OFFSET
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0,4
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LINKS
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FORMULA
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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)).
Limit_{n->oo} a(n)/a(n+1) = 0.338324339068091181557475416836618315086769320447748735003402... - Robert A. Russell, Feb 11 2023
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MAPLE
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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)):
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MATHEMATICA
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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]];
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CROSSREFS
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Cf. A000081, A001190, A000598, A036718, A036721, A036722, A182378, A244372, A292553, A292554, A292555.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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