OFFSET
4,3
COMMENTS
In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 4..1000
FORMULA
a(n) ~ c * d^n / n^(3/2), where d = 1.938950593419038561279875... and c = 0.929315638487153276953929... . - Vaclav Kotesovec, Jul 13 2014
EXAMPLE
a(7) = 4:
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MAPLE
b:= proc(n, i, h, v) option remember; `if`(n=0, `if`(v=0, 1, 0),
`if`(i<1 or v<1 or n<v, 0, add(binomial(A(i, min(i-1, h)), j)
*b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
end:
A:= proc(n, k) option remember;
`if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
end:
a:= n-> b(n-1$2, 2$2):
seq(a(n), n=4..45);
MATHEMATICA
b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i < 1 || v < 1 || n < v, 0, Sum[Binomial[A[i, Min[i - 1, h]], j] b[n - i*j, i - 1, h, v - j], {j, 0, Min[n/i, v]}]]];
A[n_, k_] := A[n, k] = If[n<2, n, Sum[b[n-1, n-1, j, j], {j, 1, Min[k, n-1] } ] ];
a[n_] := b[n-1, n-1, 2, 2];
a /@ Range[4, 45] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 12 2014
STATUS
approved