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 A006470 M2075 #61 Jul 18 2024 11:35:50
%S A006470 2,15,60,175,420,882,1680,2970,4950,7865,12012,17745,25480,35700,
%T A006470 48960,65892,87210,113715,146300,185955,233772,290950,358800,438750,
%U A006470 532350,641277,767340,912485,1078800,1268520,1484032,1727880,2002770,2311575,2657340,3043287,3472820,3949530,4477200,5059810,5701542,6406785,7180140
%N A006470 Number of tree-rooted planar maps with 3 faces and n vertices and no isthmuses.
%C A006470 a(n) is the number of ordered rooted trees with n+3 non-root nodes that have 3 leaves; see A108838. - _Joerg Arndt_, Aug 18 2014
%D A006470 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006470 Vincenzo Librandi, <a href="/A006470/b006470.txt">Table of n, a(n) for n = 1..1000</a>
%H A006470 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.
%H A006470 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A006470 a(n) = (n+1)*binomial(n+3, 4).
%F A006470 a(n) = A027789(n)/2.
%F A006470 From _Zerinvary Lajos_, Dec 14 2005: (Start)
%F A006470 a(n) = binomial(n+2, 2)*binomial(n+4, 3)/2;
%F A006470 G.f.: x*(2+3*x)/(1-x)^6. (End)
%F A006470 From _Wesley Ivan Hurt_, May 02 2015: (Start)
%F A006470 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).
%F A006470 a(n) = n*(n+1)^2*(n+2)*(n+3)/24. (End)
%F A006470 Sum_{n>=1} 1/a(n) = 61/3 - 2*Pi^2. - _Jaume Oliver Lafont_, Jul 15 2017
%F A006470 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2 - 16*log(2) + 5/3. - _Amiram Eldar_, Jan 28 2022
%p A006470 A006470:=n->(n+1)*binomial(n+3,4): seq(A006470(n), n=1..50); # _Wesley Ivan Hurt_, May 02 2015
%t A006470 Table[n (n + 1)^2 (n + 2) (n + 3) / 24, {n, 50}] (* _Vincenzo Librandi_, May 03 2015 *)
%t A006470 LinearRecurrence[{6,-15,20,-15,6,-1},{2,15,60,175,420,882},50] (* _Harvey P. Dale_, Jul 18 2024 *)
%o A006470 (Magma) [(n+1)*Binomial(n+3, 4): n in [1..30]]; // _Vincenzo Librandi_, Jun 09 2013
%Y A006470 Column 3 of A342987.
%Y A006470 Cf. A027789, A108838.
%K A006470 nonn,easy
%O A006470 1,1
%A A006470 _N. J. A. Sloane_
%E A006470 Name clarified by _Andrew Howroyd_, Apr 03 2021