A298535 Number of unlabeled rooted trees with n vertices such that every branch of the root has a different number of leaves.

1, 1, 1, 2, 5, 13, 32, 80, 200, 511, 1323, 3471, 9183, 24491, 65715, 177363, 481135, 1311340, 3589023, 9860254, 27181835, 75165194, 208439742, 579522977, 1615093755, 4511122964, 12625881944, 35405197065, 99459085125, 279861792874, 788712430532, 2226015529592

Offset

1,4

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Mathematica

rut[n_]:=rut[n]=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[rut/@c]]]/@IntegerPartitions[n-1]];
Table[Length[Select[rut[n], UnsameQ@@(Count[#, {}, {0, Infinity}]&/@#)&]], {n, 15}]

Prog

(PARI) \\ here R is A055277 as vector of polynomials
R(n) = {my(A = O(x)); for(j=1, n, A = x*(y - 1  + exp( sum(i=1, j, 1/i * subst( subst( A + x * O(x^(j\i)), x, x^i), y, y^i) ) ))); Vec(A)};
seq(n) = {my(M=Mat(apply(p->Colrev(p, n), R(n-1)))); Vec(prod(i=2, #M, 1 + x*Ser(M[i, ])))} \\ Andrew Howroyd, May 20 2018

Crossrefs

Cf. A000081, A003238, A004111, A032305, A289079, A290689, A291443, A297791, A298422, A298533, A298536.

Sequence in context: A199812 A255170 A255630 * A110320 A219230 A108890

Adjacent sequences: A298532 A298533 A298534 * A298536 A298537 A298538

Keyword

nonn

Author

Gus Wiseman, Jan 20 2018

Extensions

Terms a(19) and beyond from Andrew Howroyd, May 20 2018

Status

approved