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 A019500 #29 Apr 13 2020 13:01:30 %S A019500 1,1,1,1,1,1,6,21,56,126,252,492,1062,2667,7252,19509,49824,121019, %T A019500 286974,687384,1702308,4357383,11322408,29307458,74897808,189349041, %U A019500 477491356,1211349276,3103673406,8017385416,20780391882,53812468392,138999941172,358502419242 %N A019500 Number of 6-ary search trees on n keys. %H A019500 Alois P. Heinz, <a href="/A019500/b019500.txt">Table of n, a(n) for n = 0..700</a> %H A019500 J. A. Fill and R. P. Dobrow, <a href="https://people.carleton.edu/~rdobrow/Papers/NumberMary.pdf">The number of m-ary search trees on n keys</a>, Combin. Probab. Comput. 6 (1997), 435-453. %H A019500 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a> %F A019500 a(n) ~ c * d^n / n^(3/2), where d = 2.705312740243..., c = 0.3835479397... . - _Vaclav Kotesovec_, Sep 06 2014 %p A019500 A:= proc(n) option remember; if n=0 then 1 else convert(series( %p A019500 add(x^i, i=0..4)+ x^5*A(n-1)^6, x=0,n+1), polynom) fi %p A019500 end: %p A019500 a:= n-> coeff(A(n), x, n): %p A019500 seq(a(n), n=0..40); # _Alois P. Heinz_, Aug 22 2008 %t A019500 A[n_] := A[n] = If[n==0, 1, Series[Sum[x^i, {i, 0, 4}] + x^5*A[n-1]^6, {x, 0, n+1}] // Normal]; a[n_] := Coefficient[A[n], x, n]; Table[a[n], {n, 0, 40}] (* _Jean-François Alcover_, Feb 19 2016, after _Alois P. Heinz_ *) %K A019500 nonn %O A019500 0,7 %A A019500 James Fill (jimfill(AT)jhu.edu) %E A019500 More terms from _Alois P. Heinz_, Aug 22 2008