This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319580 Number of binary rooted trees with n leaves of n colors and all non-leaf nodes having out-degree 2. 2


%S 1,3,18,215,3600,80136,2213036,73068543,2806959015,123002168300,

%T 6055381161852,330885794632536,19872950226273053,1301261803764756855,

%U 92259974680854975000,7041606755629152575055,575638367425376279620662,50180725346542105445190603

%N Number of binary rooted trees with n leaves of n colors and all non-leaf nodes having out-degree 2.

%C Not all of the n colors need to be used.

%H Alois P. Heinz, <a href="/A319580/b319580.txt">Table of n, a(n) for n = 1..352</a>

%H V. P. Johnson, <a href="http://people.math.sc.edu/czabarka/Theses/JohnsonThesis.pdf">Enumeration Results on Leaf Labeled Trees</a>, Ph. D. Dissertation, Univ. Southern Calif., 2012.

%p A:= proc(n, k) option remember; `if`(n<2, k*n, `if`(n::odd, 0,

%p (t-> t*(1-t)/2)(A(n/2, k)))+add(A(i, k)*A(n-i, k), i=1..n/2))

%p end:

%p a:= n-> A(n$2):

%p seq(a(n), n=1..20); # _Alois P. Heinz_, Sep 23 2018

%o (PARI) a(n)={my(v=vector(n)); v[1]=n; for(n=2, n, v[n]=sum(j=1, (n-1)\2, v[j]*v[n-j]) + if(n%2, 0, binomial(v[n/2]+1, 2))); v[n]} \\ _Andrew Howroyd_, Sep 23 2018

%Y Main diagonal of A319539.

%Y Cf. A319369, A319541.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Sep 23 2018

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 12:13 EST 2019. Contains 329999 sequences. (Running on oeis4.)