A215980 - OEIS

%I #7 Dec 04 2014 07:01:41

%S 1,1,3,6,13,26,56,115,247,533,1175,2635,6037,14069,33378,80466,196759,

%T 487453,1221515,3092719,7901816,20354765,52815434,137946253,362430959,

%U 957359614,2541249138,6775848932,18141119582,48753971355,131485310625,355759469235

%N Number of simple unlabeled graphs on n nodes with exactly 10 connected components that are trees or cycles.

%H Alois P. Heinz, <a href="/A215980/b215980.txt">Table of n, a(n) for n = 10..650</a>

%e a(12) = 3: .o-o o o o o.  .o-o o o o o.  .o o o o o o.

%e            .|/         .  .|          .  .| |        .

%e            .o o o o o o.  .o o o o o o.  .o o o o o o.

%p with(numtheory):

%p b:= proc(n) option remember; local d, j; `if`(n<=1, n,

%p       (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))

%p     end:

%p g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-

%p       (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2

%p     end:

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

%p       `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*

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

%p     end:

%p a:= n-> p(n, n, 10):

%p seq(a(n), n=10..50);

%Y Column k=10 of A215977.

%Y The labeled version is A215860.

%K nonn

%O 10,3

%A _Alois P. Heinz_, Aug 29 2012