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 A007715 #36 Sep 08 2022 08:44:35
%S A007715 1,7,27,75,170,336,602,1002,1575,2365,3421,4797,6552,8750,11460,14756,
%T A007715 18717,23427,28975,35455,42966,51612,61502,72750,85475,99801,115857,
%U A007715 133777,153700,175770,200136,226952,256377,288575,323715,361971,403522,448552,497250
%N A007715 Number of 5-leaf rooted trees with n levels.
%H A007715 Vincenzo Librandi, <a href="/A007715/b007715.txt">Table of n, a(n) for n = 1..5000</a>
%H A007715 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 A007715 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A007715 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5, -10, 10, -5, 1).
%F A007715 Expansion of x*(1+2x+2x^2)/(1-x)^5.
%F A007715 a(n) = n*(n+1)*(5*n^2+n+6)/24. - _T. D. Noe_, Feb 09 2007
%F A007715 a(1)=1, a(2)=7, a(3)=27, a(4)=75, a(5)=170, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, Jul 20 2011
%F A007715 a(n) = n*A000217(n) - sum((n-3*i)*A000217(i), i=0..n-1). - _Bruno Berselli_, Jun 22 2013
%e A007715 a(7) = 7*28 - (7*0+4*1+1*3-2*6-5*10-8*15-11*21) = 602. - _Bruno Berselli_, Jun 22 2013
%t A007715 Table[n(n+1)(5n^2+n+6)/24,{n,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{1,7,27,75,170},40] (* _Harvey P. Dale_, Jul 20 2011 *)
%o A007715 (Magma) [n*(n+1)*(5*n^2+n+6)/24: n in [1..45]]; // _Vincenzo Librandi_, Jul 21 2011
%Y A007715 Row n=5 of A290353.
%K A007715 nonn,easy
%O A007715 1,2
%A A007715 _N. J. A. Sloane_, _Simon Plouffe_