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 A378804 #11 Apr 26 2025 06:00:48
%S A378804 0,8,224,5280,116480,2480640,51684864,1060899840,21541478400,
%T A378804 433812234240,8680043806720,172774871965696,3424347806171136,
%U A378804 67626404043161600,1331466198928588800,26145958720005734400,512257621575157678080,10016204637370583089152,195501127311163895316480
%N A378804 a(n) = n * 2^n * binomial(4*n, n).
%H A378804 Amiram Eldar, <a href="/A378804/b378804.txt">Table of n, a(n) for n = 0..500</a>
%H A378804 Jonathan M. Borwein and Roland Girgensohn, <a href="https://doi.org/10.1007/s00010-005-2774-x">Evaluations of binomial series</a>, aequationes mathematicae, Vol. 70, No. 1 (2005), pp. 25-36.
%F A378804 a(n) = A036289(n) * A005810(n).
%F A378804 a(n) = 2^n * A378802(n).
%F A378804 a(n) == 0 (mod 8).
%F A378804 Sum_{n>=1} (-1)^n/a(n) = (log(2) - 6*log(3))/7 + Sum_{r: 2*r^3 + 12*r + 13 = 0} log(r+2)/(r+3) = -0.120716907732393305... (Borwein and Girgensohn, 2005, p. 32, eq. (43)).
%t A378804 a[n_] := n * 2^n * Binomial[4*n, n]; Array[a, 20, 0]
%o A378804 (PARI) a(n) = n * 2^n * binomial(4*n, n);
%Y A378804 Cf. A005810, A036289, A378802.
%K A378804 nonn,easy
%O A378804 0,2
%A A378804 _Amiram Eldar_, Dec 07 2024