cp's OEIS Frontend

A244398 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 2.

%I A244398 #13 Feb 09 2015 10:48:26
%S A244398 1,2,5,10,22,45,97,206,450,982,2178,4849,10904,24630,56010,127911,
%T A244398 293546,676156,1563371,3626148,8436378,19680276,46026617,107890608,
%U A244398 253450710,596572386,1406818758,3323236237,7862958390,18632325318,44214569099,105061603968
%N A244398 Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 2.
%H A244398 Alois P. Heinz, <a href="/A244398/b244398.txt">Table of n, a(n) for n = 3..1000</a>
%F A244398 a(n) = A001190(n+1)-1 = A036656(n+1)-1.
%F A244398 a(n) ~ c * d^n / n^(3/2), where d = 2.4832535361726368... = A086317 and c = 0.7916031835775118... = A086318. - _Vaclav Kotesovec_, Jun 27 2014
%p A244398 b:= proc(n, i, t, k) option remember; `if`(n=0, 1,
%p A244398       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
%p A244398        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))
%p A244398     end:
%p A244398 a:= n-> b(n-1$2, 2$2) -`if`(n=0, 0, 1):
%p A244398 seq(a(n), n=3..40);
%t A244398 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 *)
%Y A244398 Column k=2 of A244372.
%Y A244398 Cf. A001190, A036656, A086317, A086318.
%K A244398 nonn
%O A244398 3,2
%A A244398 _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014