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 A384129 #12 May 23 2025 03:57:37 %S A384129 1,3,85,4536,357423,37312275,4853222764,756111184500,137272511800831, %T A384129 28460103232088385,6634460278534540725,1717750737160208150400, %U A384129 489078062391738506912340,151874660255802127280374140,51082995429153110239690350120,18500755859447038660174079965500 %N A384129 Number of permutations of 3*n objects with exactly 2*n cycles. %F A384129 a(n) = A132393(3*n,2*n) = |Stirling1(3*n,2*n)|. %F A384129 a(n) = (3*n)! * [x^(3*n)] log(1 - x)^(2*n) / (2*n)!. %F A384129 a(n) ~ 3^(4*n - 1/2) * w^(3*n) * n^(n - 1/2) / (sqrt(Pi*(w-1)) * 2^(2*n + 1/2) * exp(n) * (3*w-2)^n), where w = -LambertW(-1, -2*exp(-2/3)/3) = 1.4293552275170056487... - _Vaclav Kotesovec_, May 23 2025 %o A384129 (PARI) a(n) = abs(stirling(3*n, 2*n, 1)); %Y A384129 Cf. A132393, A187646, A348084. %K A384129 nonn,easy %O A384129 0,2 %A A384129 _Seiichi Manyama_, May 20 2025