OFFSET
0,6
COMMENTS
Number of free trees with n nodes, each node with degree <= n-2. - Robert A. Russell, Jan 25 2023
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 20 2008
STATUS
approved