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 A384171 #9 May 21 2025 06:39:52
%S A384171 1,18,503,19312,946009,56419200,3967700295,321506211840,
%T A384171 29497821190065,3022798062551040,342204383046633975,
%U A384171 42414460290839347200,5712600791700063700425,830773593435129407078400,129744737403826992957167175,21657021896289762215460864000,3847769544999445159548440534625
%N A384171 a(n) = 2^n * n! * binomial(5*n/2,n) * Sum_{k=1..n} 1/(3*n+2*k).
%F A384171 a(n) = Sum_{k=0..n} k * (3*n+2)^(k-1) * 2^(n-k) * |Stirling1(n,k)|.
%F A384171 a(n) = n! * [x^n] ( -log(1 - 2*x)/(2 * (1 - 2*x)^(3*n/2+1)) ).
%o A384171 (PARI) a(n) = sum(k=0, n, k*(3*n+2)^(k-1)*2^(n-k)*abs(stirling(n, k, 1)));
%Y A384171 Cf. A384137, A384172.
%K A384171 nonn
%O A384171 1,2
%A A384171 _Seiichi Manyama_, May 21 2025