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 A383883 #17 May 14 2025 09:08:19
%S A383883 1,1,11,222,6627,262570,12978758,769079444,53138842515,4194648739710,
%T A383883 372421403333850,36733739199892020,3985122473105099406,
%U A383883 471598870326072262644,60456151456891375730860,8345905345383943433713800,1234395864446065862689721475,194738649118647202909304657910
%N A383883 a(n) = [x^n] 1/((1 - n*x) * Product_{k=0..n-1} (1 - k*x)^2).
%F A383883 a(n) = Sum_{k=0..n} Stirling2(n+k-1,n-1) * Stirling2(2*n-k,n) for n > 0.
%F A383883 a(n) = A287532(n,n).
%F A383883 a(n) ~ 3^(3*n - 1/2) * n^(n - 1/2) / (sqrt(Pi*(1-w)) * 2^(2*n + 1/2) * exp(n) * (3 - 2*w)^n * w^(2*n - 1/2)), where w = -LambertW(-3*exp(-3/2)/2). - _Vaclav Kotesovec_, May 14 2025
%t A383883 Join[{1}, Table[Sum[StirlingS2[n + k - 1, n - 1]*StirlingS2[2*n - k, n], {k, 0, n}], {n, 1, 20}]] (* _Vaclav Kotesovec_, May 14 2025 *)
%o A383883 (PARI) a(n) = polcoef(1/((1-n*x)*prod(k=0, n-1, 1-k*x+x*O(x^n))^2), n);
%Y A383883 Cf. A350376, A383880.
%Y A383883 Cf. A187235, A287532.
%K A383883 nonn
%O A383883 0,3
%A A383883 _Seiichi Manyama_, May 13 2025