A318754 -id:A318754 - cp's OEIS frontend

A318824 Number of rooted trees with n nodes such that nine equals the maximal number of subtrees of the same size extending from the same node.

0, 1, 1, 3, 8, 22, 60, 167, 465, 1306, 3682, 10423, 29597, 84309, 240735, 688941, 1975403, 5673911, 16322021, 47018402, 135613575, 391590057, 1131902512, 3274898117, 9483405678, 27483959193, 79710664789, 231340909288, 671840817408, 1952268260256, 5676162227486

Offset: 9

Alois P. Heinz, Sep 04 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 9..2138

Column k=9 of A318754.

g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
    end:
a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(9):
seq(a(n), n=9..39);

A318825 Number of rooted trees with n nodes such that ten equals the maximal number of subtrees of the same size extending from the same node.

Original entry on oeis.org

0, 1, 1, 3, 8, 22, 60, 167, 465, 1306, 3681, 10423, 29598, 84313, 240753, 689013, 1975659, 5674795, 16324964, 47028023, 135644560, 391688795, 1132214229, 3275875477, 9486452270, 27493411521, 79739873360, 231430860268, 672117013805, 1953114161607, 5678747123701

Offset: 10

Alois P. Heinz, Sep 04 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 10..2139

Column k=10 of A318754.

g:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      binomial(g(i-1$2, k)+j-1, j)*g(n-i*j, i-1, k), j=0..min(k, n/i))))
    end:
a:= n-> (k-> g(n-1$2, k) -g(n-1$2, k-1))(10):
seq(a(n), n=10..40);

cp's OEIS Frontend

A318824 Number of rooted trees with n nodes such that nine equals the maximal number of subtrees of the same size extending from the same node.

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