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 A378781 #15 Apr 26 2025 06:01:04
%S A378781 0,2,160,6048,168960,4004000,85542912,1701719040,32133218304,
%T A378781 583116019200,10255365120000,175853140869120,2953078190899200,
%U A378781 48728661198077952,792158036489666560,12713192776728576000,201760465448645689344,3170643145439310643200,49394436443159427809280
%N A378781 a(n) = n^3 * 2^n * binomial(3*n, n) / 3.
%H A378781 Amiram Eldar, <a href="/A378781/b378781.txt">Table of n, a(n) for n = 0..500</a>
%H A378781 D. V. Chudnovsky and G. V. Chudnovsky, <a href="https://doi.org/10.1073/pnas.95.6.2744">Classification of hypergeometric identities for Pi and other logarithms of algebraic numbers</a>, Proceedings of the National Academy of Sciences, Vol. 95, No. 6 (1998), pp. 2744-2749. See p. 2749.
%F A378781 a(n) = A128789(n) * A005809(n) / 3.
%F A378781 a(n) = n * A378778(n) / 3.
%F A378781 a(n) = n^2 * A378780(n) / 3.
%F A378781 Sum_{n>=1} 1/a(n) = 3*G*Pi - Pi^2*log(2)/8 + log(2)^3/2 - 99*zeta(3)/16, where G is Catalan's constant (Chudnovsky and Chudnovsky, 1998).
%t A378781 a[n_] := n^3 * 2^n * Binomial[3*n, n] / 3; Array[a, 25, 0]
%o A378781 (PARI) a(n) = n^3 * 2^n * binomial(3*n, n) / 3;
%Y A378781 Cf. A005809, A128789, A378778, A378780.
%Y A378781 Cf. A002117, A006752.
%K A378781 nonn,easy
%O A378781 0,2
%A A378781 _Amiram Eldar_, Dec 07 2024