A144520 a(n) = A000055(n) - 1.

0, 0, 0, 0, 1, 2, 5, 10, 22, 46, 105, 234, 550, 1300, 3158, 7740, 19319, 48628, 123866, 317954, 823064, 2144504, 5623755, 14828073, 39299896, 104636889, 279793449, 751065459, 2023443031, 5469566584, 14830871801, 40330829029, 109972410220, 300628862479

Offset

0,6

Comments

Number of free trees with n nodes, each node with degree <= n-2. - Robert A. Russell, Jan 25 2023

Links

Table of n, a(n) for n=0..33.

Rebecca Neville, Graphs whose vertices are forests with bounded degree, Graph Theory Notes of New York, LIV (2008), 12-21. [Wayback Machine link]

Formula

a(n) = A144528(n,n-2). - Robert A. Russell, Jan 25 2023

Mathematica

b[n_, i_, t_, k_] := b[n, i, t, k] = 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]}]];
  b[0, i_, t_, k_] = 1;
Join[{0, 0, 0, 0, 1}, Table[m = n - 3;
  gf[x_] := 1 + Sum[b[j - 1, j - 1, m, m] x^j, {j, 1, n}];
  ci[x_] := SymmetricGroupIndex[m + 1, x] /. x[i_] -> gf[x^i];
  SeriesCoefficient[Series[gf[x] - (gf[x]^2 - gf[x^2])/2 + x ci[x],
{x, 0, n}], n], {n, 5, 35}]] (* Robert A. Russell, Jan 25 2023 *)

Crossrefs

Cf. A000055, A144528.

Sequence in context: A100938 A018004 A124329 * A101399 A320650 A018109

Adjacent sequences: A144517 A144518 A144519 * A144521 A144522 A144523

Keyword

nonn

Author

N. J. A. Sloane, Dec 20 2008

Status

approved