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 A384207 #11 May 22 2025 17:12:46
%S A384207 1,10,6562,21157758,192817813260,3803916720008250,
%T A384207 138757892706447212551,8432782489668636227456524,
%U A384207 792912489591430219972681508172,109146372957847294924041235504625400,21071987342698034891951000233099719150440,5513873439400596105839885628799257242723984298
%N A384207 a(n) = [x^(3*n)] Product_{k=0..n} 1/(1 - k*x)^3.
%F A384207 a(n) = Sum_{i=0..3*n, j=0..3*n-i} Stirling2(i+n, n) * Stirling2(j+n, n) * Stirling2(4*n-i-j, n).
%F A384207 a(n) ~ 2^(6*n + 1/2) * n^(3*n - 1/2) / (sqrt(3*Pi*(1-w)) * w^(3*n+1) * exp(3*n) * (2-w)^(3*n)), where w = -LambertW(-2*exp(-2)) = -A226775 = 0.406375739959959907676958124124839758210...
%t A384207 Table[SeriesCoefficient[Product[1/(1-k*x)^3, {k, 0, n}], {x, 0, 3*n}], {n, 0, 15}]
%t A384207 Table[Sum[StirlingS2[i+n, n] * StirlingS2[j+n, n] * StirlingS2[4*n-i-j, n], {i, 0, 3*n}, {j, 0, 3*n-i}], {n, 0, 15}]
%Y A384207 Cf. A007820, A383862, A384022, A384206.
%K A384207 nonn
%O A384207 0,2
%A A384207 _Vaclav Kotesovec_, May 22 2025