A244404 - OEIS

%I #8 Feb 09 2015 11:03:16

%S 1,2,6,17,50,143,416,1199,3473,10042,29089,84259,244316,708679,

%T 2057087,5974077,17359390,50467157,146789962,427148444,1243513350,

%U 3621591235,10551595959,30753712080,89666493709,261522175986,763002239120,2226771020793,6500575182332

%N Number of unlabeled rooted trees with n nodes and maximal outdegree (branching factor) 8.

%H Alois P. Heinz, <a href="/A244404/b244404.txt">Table of n, a(n) for n = 9..750</a>

%p b:= proc(n, i, t, k) option remember; `if`(n=0, 1,

%p       `if`(i<1, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*

%p        b(n-i*j, i-1, t-j, k), j=0..min(t, n/i))))

%p     end:

%p a:= n-> b(n-1$2, 8$2) -`if`(k=0, 0, b(n-1$2, 7$2)):

%p seq(a(n), n=9..40);

%t 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, 8, 8] - If[n == 0, 0, b[n - 1, n - 1, 7, 7]]; Table[a[n], {n, 9, 40}] (* _Jean-François Alcover_, Feb 09 2015, after Maple *)

%Y Column k=8 of A244372.

%K nonn

%O 9,2

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 27 2014