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 A384170 #9 May 21 2025 06:39:36
%S A384170 1,17,423,14198,603194,31069980,1882538440,131223122480,
%T A384170 10345975290000,910393948446560,88452245803947200,9405081915991747200,
%U A384170 1086351888729412883200,135456246872643979788800,18134220756665496528460800,2594357788916663689703168000,395006034401484168868002560000
%N A384170 a(n) = 3^n * n! * binomial(5*n/3,n) * Sum_{k=1..n} 1/(2*n+3*k).
%F A384170 a(n) = Sum_{k=0..n} k * (2*n+3)^(k-1) * 3^(n-k) * |Stirling1(n,k)|.
%F A384170 a(n) = n! * [x^n] ( -log(1 - 3*x)/(3 * (1 - 3*x)^(2*n/3+1)) ).
%o A384170 (PARI) a(n) = sum(k=0, n, k*(2*n+3)^(k-1)*3^(n-k)*abs(stirling(n, k, 1)));
%Y A384170 Cf. A384136.
%K A384170 nonn
%O A384170 1,2
%A A384170 _Seiichi Manyama_, May 21 2025