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A244398
Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 2.
2
1, 2, 5, 10, 22, 45, 97, 206, 450, 982, 2178, 4849, 10904, 24630, 56010, 127911, 293546, 676156, 1563371, 3626148, 8436378, 19680276, 46026617, 107890608, 253450710, 596572386, 1406818758, 3323236237, 7862958390, 18632325318, 44214569099, 105061603968
OFFSET
3,2
LINKS
FORMULA
a(n) = A001190(n+1)-1 = A036656(n+1)-1.
a(n) ~ c * d^n / n^(3/2), where d = 2.4832535361726368... = A086317 and c = 0.7916031835775118... = A086318. - Vaclav Kotesovec, Jun 27 2014
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
end:
a:= n-> b(n-1$2, 2$2) -`if`(n=0, 0, 1):
seq(a(n), n=3..40);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, 1, 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]}]] // FullSimplify]; a[n_] := b[n-1, n-1, 2, 2] - If[n == 0, 0, 1]; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Feb 09 2015, after Maple *)
CROSSREFS
Column k=2 of A244372.
Sequence in context: A045621 A026655 A336484 * A100938 A018004 A124329
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 27 2014
STATUS
approved