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 A134171 #40 Sep 24 2022 05:47:38
%S A134171 0,0,0,27,108,270,540,945,1512,2268,3240,4455,5940,7722,9828,12285,
%T A134171 15120,18360,22032,26163,30780,35910,41580,47817,54648,62100,70200,
%U A134171 78975,88452,98658,109620,121365,133920,147312,161568,176715,192780,209790,227772,246753
%N A134171 a(n) = (9/2)*(n-1)*(n-2)*(n-3).
%C A134171 Number of n permutations (n>=3) of 4 objects u, v, z, x with repetition allowed, containing n-3=0 u's. Example: if n=3 then n-3 =zero u, a()=27 because we have vzx, vxz, zvx, zxv, xvz, xzv, vvv, zzz, xxx, vvx, vxv, xvv, xxv, xvx, vxx, vvz, vzv, zvv, zzv, zvz, vzz, xzz, zxz, zzx, xxz, xzx, zxx. A027465 formatted as a triangular array: diagonal: 27, 108, 270, 540, 945, 1512. - _Zerinvary Lajos_, Aug 06 2008
%H A134171 G. C. Greubel, <a href="/A134171/b134171.txt">Table of n, a(n) for n = 1..1000</a>
%H A134171 D. Zvonkine, <a href="http://www.math.jussieu.fr/~zvonkine/">Home Page</a>.
%H A134171 D. Zvonkine, <a href="http://mi.mathnet.ru/eng/mmj274">Counting ramified coverings and intersection theory on Hurwitz spaces II (local structure of Hurwitz spaces and combinatorial results)</a>, Moscow Mathematical Journal, Vol. 7, No. 1 (2007), 135-162.
%H A134171 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A134171 a(n) = 27 * binomial(n-1,3). - _Zerinvary Lajos_, Aug 06 2008
%F A134171 From _Chai Wah Wu_, May 29 2016: (Start)
%F A134171 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A134171 G.f.: 27*x^4/(1-x)^4. (End)
%F A134171 E.g.f.: 27 + (9/2*(x^3-3*x^2+6*x-6))*exp(x). - _G. C. Greubel_, May 17 2021
%F A134171 a(n) = 27 * A000292(n-3) for n >= 3. - _Alois P. Heinz_, May 17 2021
%F A134171 From _Amiram Eldar_, Sep 24 2022: (Start)
%F A134171 Sum_{n>=4} 1/a(n) = 1/18.
%F A134171 Sum_{n>=4} (-1)^n/a(n) = 4*log(2)/9 - 5/18. (End)
%p A134171 seq(27*binomial(n-1, 3), n=1..30); # _Zerinvary Lajos_, May 18 2008
%t A134171 LinearRecurrence[{4,-6,4,-1}, {0,0,0,27}, 50] (* _G. C. Greubel_, May 29 2016 *)
%o A134171 (Magma) [(9/2)*(n-1)*(n-2)*(n-3) : n in [1..50]]; // _Wesley Ivan Hurt_, May 29 2016
%Y A134171 Cf. A008585, A027465, A027468. - _Zerinvary Lajos_, Aug 06 2008
%Y A134171 Cf. A000292, A102741, A113335.
%K A134171 nonn,easy
%O A134171 1,4
%A A134171 _N. J. A. Sloane_, Jan 30 2008