A032028 Number of rooted planar trees (n+1 nodes) where any 2 subtrees extending from same node are different.

1, 1, 1, 2, 4, 9, 23, 62, 167, 461, 1309, 3784, 11018, 32431, 96294, 288246, 868107, 2629499, 8005166, 24482202, 75177313, 231697259, 716488213, 2222381516, 6912569477, 21556270329, 67380727837, 211080434346

Offset: 1

Author

Christian G. Bower

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• C. G. Bower, Transforms (2)
• Index entries for sequences related to rooted trees

Programs

PARI

AGK(v)={apply(p->subst(serlaplace(y^0*p),y,1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}
CGK(v)={apply(p->subst(serlaplace(p/y),y,1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}
seq(n)={my(v=[1]); for(i=3, n, v=concat([1], AGK(v))); concat([1], CGK(v))} \\ Andrew Howroyd, Sep 20 2018

Formula

"CGK" (necklace, elements, unlabeled) transform of A032027 (shifted right one place).