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A298535 Number of unlabeled rooted trees with n vertices such that every branch of the root has a different number of leaves. 4
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 (list; graph; refs; listen; history; text; internal format)
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,changed

AUTHOR

Gus Wiseman, Jan 20 2018

EXTENSIONS

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

STATUS

approved

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Last modified May 26 05:17 EDT 2018. Contains 304593 sequences. (Running on oeis4.)