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 A192849 #33 Feb 16 2025 08:33:15
%S A192849 0,0,24,240,1080,3360,8400,18144,35280,63360,106920,171600,264264,
%T A192849 393120,567840,799680,1101600,1488384,1976760,2585520,3335640,4250400,
%U A192849 5355504,6679200,8252400,10108800,12285000,14820624,17758440,21144480
%N A192849 Molecular topological indices of the triangular graphs.
%C A192849 Triangular graphs are defined for n>=2; extended to n=1 using closed form.
%H A192849 Reinhard Zumkeller, <a href="/A192849/b192849.txt">Table of n, a(n) for n = 1..10000</a>
%H A192849 G. D. Birkhoff, <a href="https://www.jstor.org/stable/1967597">A determinant formula for the number of ways of coloring a map</a>, Ann. Math., 14:42-4. See 2nd polynomial p. 5.
%H A192849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>.
%H A192849 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A192849 a(n) = n*(n^2 - 1)*(n-2)^2.
%F A192849 a(n) = 24*A027800(n-3).
%F A192849 G.f.: 24*x^3*(4*x+1)/(x-1)^6. - _Colin Barker_, Aug 07 2012
%F A192849 a(n) = A245334(n+1,4), n > 2. - _Reinhard Zumkeller_, Aug 31 2014
%F A192849 E.g.f.: x^3*(4 + 6*x + x^2)*exp(x). - _G. C. Greubel_, Jan 05 2019
%F A192849 From _Amiram Eldar_, May 14 2022: (Start)
%F A192849 Sum_{n>=3} 1/a(n) = Pi^2/36 - 49/216.
%F A192849 Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2/72 - 10*log(2)/9 + 145/216. (End)
%p A192849 [n*(n^2-1)*(n-2)^2$n=1..40]; # _Muniru A Asiru_, Jan 05 2019
%t A192849 Table[n*(n^2-1)*(n-2)^2, {n,1,40}] (* _G. C. Greubel_, Jan 05 2019 *)
%o A192849 (Haskell)
%o A192849 a192849 n = if n < 3 then 0 else a245334 (n + 1) 4
%o A192849 -- _Reinhard Zumkeller_, Aug 31 2014
%o A192849 (PARI) vector(40, n, n*(n^2 -1)*(n-2)^2) \\ _G. C. Greubel_, Jan 05 2019
%o A192849 (Magma) [n*(n^2 -1)*(n-2)^2: n in [1..40]]; // _G. C. Greubel_, Jan 05 2019
%o A192849 (Sage) [n*(n^2 -1)*(n-2)^2 for n in (1..40)] # _G. C. Greubel_, Jan 05 2019
%o A192849 (GAP) List([1..40], n -> n*(n^2 -1)*(n-2)^2); # _G. C. Greubel_, Jan 05 2019
%Y A192849 Cf. A027800, A245334.
%K A192849 nonn,easy
%O A192849 1,3
%A A192849 _Eric W. Weisstein_, Jul 11 2011