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 A378779 #11 Mar 31 2025 02:55:33
%S A378779 0,12,960,48384,2027520,76876800,2737373184,93351444480,3084788957184,
%T A378779 99518467276800,3150448164864000,98221972499988480,
%U A378779 3023952067480780800,92119659815689519104,2781153700681435054080,83317180181568395673600,2479232599432958230659072,73338095004533174933913600
%N A378779 a(n) = n^2 * 4^n * binomial(3*n, n).
%H A378779 Amiram Eldar, <a href="/A378779/b378779.txt">Table of n, a(n) for n = 0..500</a>
%H A378779 Necdet Batir, <a href="https://doi.org/10.1007/BF02829799">On the series Sum_{k=1..oo} binomial(3k,k)^{-1} k^{-n} x^k</a>, Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4 (2005), pp. 371-381; <a href="https://arxiv.org/abs/math/0512310">arXiv preprint</a>, arXiv:math/0512310 [math.AC], 2005.
%F A378779 a(n) = A128782(n) * A005809(n).
%F A378779 a(n) = n^2 * A006588(n).
%F A378779 a(n) == 0 (mod 12).
%F A378779 Sum_{n>=1} (-1)^n/a(n) = 6 * arccot(2*sqrt(3)+sqrt(7))^2 - log(2)^2/2 (Batir, 2005, p. 379, eq. (3.8)).
%t A378779 a[n_] := n^2 * 4^n * Binomial[3*n, n]; Array[a, 25, 0]
%o A378779 (PARI) a(n) = n^2 * 4^n * binomial(3*n, n);
%Y A378779 Cf. A005809, A006588, A128782.
%K A378779 nonn,easy
%O A378779 0,2
%A A378779 _Amiram Eldar_, Dec 07 2024