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 A006411 M3073 #62 Aug 02 2024 22:39:38
%S A006411 3,20,75,210,490,1008,1890,3300,5445,8580,13013,19110,27300,38080,
%T A006411 52020,69768,92055,119700,153615,194810,244398,303600,373750,456300,
%U A006411 552825,665028,794745,943950,1114760,1309440,1530408,1780240,2061675,2377620,2731155,3125538
%N A006411 Number of nonseparable tree-rooted planar maps with n + 2 edges and 3 vertices.
%D A006411 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006411 Vincenzo Librandi, <a href="/A006411/b006411.txt">Table of n, a(n) for n = 1..1000</a>
%H A006411 T. R. S. Walsh and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B, Vol. 18, No. 3 (1975), pp. 222-259. See Table IVa.
%H A006411 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A006411 G.f.: x*(3+2*x)/(1-x)^6.
%F A006411 a(n) = n*(n+1)*(n+2)^2*(n+3)/24. - _Bruno Berselli_, May 17 2011
%F A006411 a(n) = A027777(n)/2. - _Zerinvary Lajos_, Mar 23 2007
%F A006411 a(n) = binomial(n+2,n)*binomial(n+2,n-1) - binomial(n+2,n+1)*binomial(n+2,n-2). - _J. M. Bergot_, Apr 07 2013
%F A006411 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Harvey P. Dale_, Dec 24 2013
%F A006411 Sum_{n>=1} 1/a(n) = 2*Pi^2 - 58/3. - _Jaume Oliver Lafont_, Jul 15 2017
%F A006411 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 + 16*log(2) - 62/3. - _Amiram Eldar_, Jan 28 2022
%p A006411 A006411:=n->n*(n+1)*(n+2)^2*(n+3)/24: seq(A006411(n), n=1..50); # _Wesley Ivan Hurt_, Jul 15 2017
%t A006411 CoefficientList[Series[x (3+2x)/(1-x)^6,{x,0,40}],x] (* or *) LinearRecurrence[ {6,-15,20,-15,6,-1},{0,3,20,75,210,490},40] (* _Harvey P. Dale_, Dec 24 2013 *)
%o A006411 (Magma) [n*(n+1)*(n+2)^2*(n+3)/24: n in [1..50]]; // _Vincenzo Librandi_, May 19 2011
%Y A006411 Column 3 of A342984.
%Y A006411 Cf. A006412, A006413, A027777.
%K A006411 nonn,easy,nice
%O A006411 1,1
%A A006411 _N. J. A. Sloane_
%E A006411 G.f. adapted to the offset by _Bruno Berselli_, May 17 2011