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 A384168 #9 May 21 2025 06:39:09
%S A384168 1,13,234,5566,165944,5966136,251491120,12169996912,665146831680,
%T A384168 40530954643840,2724842629685120,200361647815660800,
%U A384168 15997170878205905920,1378271357428552115200,127459020533529062246400,12593128815600367187507200,1323895109721239722075136000
%N A384168 a(n) = 3^n * n! * binomial(4*n/3,n) * Sum_{k=1..n} 1/(n+3*k).
%F A384168 a(n) = Sum_{k=0..n} k * (n+3)^(k-1) * 3^(n-k) * |Stirling1(n,k)|.
%F A384168 a(n) = n! * [x^n] ( -log(1 - 3*x)/(3 * (1 - 3*x)^(n/3+1)) ).
%o A384168 (PARI) a(n) = sum(k=0, n, k*(n+3)^(k-1)*3^(n-k)*abs(stirling(n, k, 1)));
%Y A384168 Cf. A098118, A384167, A384169.
%Y A384168 Cf. A303486.
%K A384168 nonn
%O A384168 1,2
%A A384168 _Seiichi Manyama_, May 21 2025