This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007713 #42 Jul 08 2025 01:01:41
%S A007713 1,1,4,10,30,75,206,518,1344,3357,8429,20759,51044,123973,299848,
%T A007713 719197,1716563,4070800,9607797,22555988,52718749,122655485,284207304,
%U A007713 655894527,1508046031,3454808143,7887768997,17949709753,40719611684,92096461012,207697731344
%N A007713 Number of 4-level rooted trees with n leaves.
%H A007713 Alois P. Heinz, <a href="/A007713/b007713.txt">Table of n, a(n) for n = 0..1000</a>
%H A007713 P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H A007713 B. A. Huberman and T. Hogg, <a href="https://doi.org/10.1016/0167-2789(86)90308-1">Complexity and adaptation</a>, Evolution, games and learning (Los Alamos, N.M., 1985). Phys. D 22 (1986), no. 1-3, 376-384.
%H A007713 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A007713 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A007713 Euler transform applied thrice to all-1's sequence.
%e A007713 From _Gus Wiseman_, Oct 11 2018: (Start)
%e A007713 Also the number of multiset partitions of multiset partitions of integer partitions of n. For example, the a(1) = 1 through a(4) = 30 multiset partitions are:
%e A007713 ((1)) ((2)) ((3)) ((4))
%e A007713 ((11)) ((12)) ((13))
%e A007713 ((1)(1)) ((111)) ((22))
%e A007713 ((1))((1)) ((1)(2)) ((112))
%e A007713 ((1)(11)) ((1111))
%e A007713 ((1))((2)) ((1)(3))
%e A007713 ((1))((11)) ((2)(2))
%e A007713 ((1)(1)(1)) ((1)(12))
%e A007713 ((1))((1)(1)) ((2)(11))
%e A007713 ((1))((1))((1)) ((1)(111))
%e A007713 ((11)(11))
%e A007713 ((1))((3))
%e A007713 ((2))((2))
%e A007713 ((1))((12))
%e A007713 ((1)(1)(2))
%e A007713 ((2))((11))
%e A007713 ((1))((111))
%e A007713 ((1)(1)(11))
%e A007713 ((11))((11))
%e A007713 ((1))((1)(2))
%e A007713 ((2))((1)(1))
%e A007713 ((1))((1)(11))
%e A007713 ((1)(1)(1)(1))
%e A007713 ((11))((1)(1))
%e A007713 ((1))((1))((2))
%e A007713 ((1))((1))((11))
%e A007713 ((1))((1)(1)(1))
%e A007713 ((1)(1))((1)(1))
%e A007713 ((1))((1))((1)(1))
%e A007713 ((1))((1))((1))((1))
%e A007713 (End)
%p A007713 with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d,j; if n=0 then 1 else add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: b0:= etr(1): b1:= etr(b0): a:= etr(b1): seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 08 2008
%t A007713 i[ n_, m_ ] := 1 /; m==1 || n==0; i[ n_, m_ ] := (i[ n, m ]=1/n Sum[ i[ k, m ] Plus @@ ((# i[ #, m-1 ])& /@ Divisors[ n-k ]), {k, 0, n-1} ]) /; n>0 && m>1
%t A007713 etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[ j]}]*b[n-j], {j, 1, n}]/n]; b]; b0 = etr[Function[1]]; b1 = etr[b0]; a = etr[b1]; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Mar 05 2015, after _Alois P. Heinz_ *)
%Y A007713 Column k=4 of A290353.
%Y A007713 Main diagonal of A055886.
%Y A007713 Cf. A001970, A047968, A050342, A089259, A141268, A258466, A261049, A319066, A320328, A320330, A320331.
%K A007713 easy,nonn
%O A007713 0,3
%A A007713 _N. J. A. Sloane_