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 A298533 Number of unlabeled rooted trees with n vertices such that every branch of the root has the same number of leaves. 6
 1, 1, 2, 4, 8, 15, 31, 64, 144, 333, 808, 2004, 5109, 13199, 34601, 91539, 244307, 656346, 1774212, 4820356, 13157591, 36060811, 99198470, 273790194, 757971757, 2104222594, 5856496542, 16338140048, 45678276507, 127964625782, 359155302204, 1009790944307 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..500 EXAMPLE The a(5) = 8 trees: ((((o)))), (((oo))), ((o(o))), ((ooo)), (o((o))), ((o)(o)), (oo(o)), (oooo) MATHEMATICA rut[n_]:=rut[n]=If[n===1, {{}}, Join@@Function[c, Union[Sort/@Tuples[rut/@c]]]/@IntegerPartitions[n-1]]; Table[Length[Select[rut[n], SameQ@@(Count[#, {}, {0, Infinity}]&/@#)&]], {n, 15}] PROG (PARI) \\ here R is A055277 as vector of polynomials EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} 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)))); concat([1], sum(i=2, #M, EulerT(M[i, ])))} \\ Andrew Howroyd, May 20 2018 CROSSREFS Cf. A000081, A003238, A004111, A032305, A289079, A290689, A291443, A297791, A298422, A298534, A298535. Sequence in context: A300520 A243082 A092603 * A259805 A086125 A227236 Adjacent sequences: A298530 A298531 A298532 * A298534 A298535 A298536 KEYWORD nonn 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 December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)