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A318859 Number of rooted trees with n nodes such that two equals the maximal number of isomorphic subtrees extending from the same node. 3
0, 1, 1, 4, 9, 22, 54, 138, 346, 889, 2285, 5928, 15436, 40424, 106230, 280305, 741912, 1969816, 5243942, 13995807, 37439883, 100371907, 269623436, 725638613, 1956352468, 5283171593, 14289645110, 38707131195, 104995130162, 285184002486, 775586517781 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,4
LINKS
MAPLE
h:= proc(n, m, t, k) option remember; `if`(m=0, binomial(n+t, t),
`if`(n=0, 0, add(h(n-1, m-j, t+1, k), j=1..min(k, m))))
end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1, k)*h(A(i, k), j, 0, k), j=0..n/i)))
end:
A:= (n, k)-> `if`(n<2, n, b(n-1$2, k)):
a:= n-> (k-> A(n, k)-A(n, k-1))(2):
seq(a(n), n=2..32);
MATHEMATICA
h[n_, m_, t_, k_] := h[n, m, t, k] = If[m == 0, Binomial[n + t, t],
If[n == 0, 0, Sum[h[n - 1, m - j, t + 1, k], {j, 1, Min[k, m]}]]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0,
Sum[b[n - i*j, i - 1, k]*h[A[i, k], j, 0, k], {j, 0, n/i}]]];
A[n_, k_] := If[n < 2, n, b[n - 1, n - 1, k]];
a[n_] := A[n, 2] - A[n, 1];
Table[a[n], {n, 2, 32}] (* Jean-François Alcover, Dec 01 2023, after Alois P. Heinz *)
CROSSREFS
Column k=2 of A318758.
Sequence in context: A076859 A042833 A048654 * A318817 A122626 A135025
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 04 2018
STATUS
approved

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Last modified February 20 21:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)