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

1,4

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

Formula

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

Prog

(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

Crossrefs

Sequence in context: A339296 A213683 A032010 * A190277 A274882 A127384

Adjacent sequences: A032025 A032026 A032027 * A032029 A032030 A032031

Keyword

nonn

Author

Christian G. Bower

Status

approved