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 A383880 #12 May 14 2025 04:08:42
%S A383880 1,0,3,72,2307,95060,4817990,290523576,20333487251,1621036680120,
%T A383880 145057745669850,14399349523416000,1570425994090538574,
%U A383880 186674663305762642296,24021930409036829669036,3327140929951823209016400,493515678917684006649451651,78054583374364036172432641200
%N A383880 a(n) = [x^n] 1/Product_{k=0..n-1} (1 - k*x)^2.
%F A383880 a(n) = Sum_{k=0..n} Stirling2(n+k-1,n-1) * Stirling2(2*n-k-1,n-1) for n > 0.
%F A383880 a(n) ~ 3^(3*n - 3/2) * n^(n - 1/2) / (sqrt(Pi*(1-w)) * 2^(2*n - 1/2) * exp(n) * (3 - 2*w)^n * w^(2*n - 3/2)), where w = -LambertW(-3*exp(-3/2)/2). - _Vaclav Kotesovec_, May 14 2025
%t A383880 Join[{1}, Table[Sum[StirlingS2[n + k - 1, n - 1]*StirlingS2[2*n - k - 1, n - 1], {k, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, May 14 2025 *)
%o A383880 (PARI) a(n) = polcoef(1/prod(k=0, n-1, 1-k*x+x*O(x^n))^2, n);
%Y A383880 Cf. A350376, A383883.
%Y A383880 Cf. A342111.
%K A383880 nonn
%O A383880 0,3
%A A383880 _Seiichi Manyama_, May 13 2025