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 A384022 #13 May 22 2025 05:27:33
%S A384022 1,6,699,242434,170580831,202617635850,364680579642546,
%T A384022 926271490234962816,3156974021179142865351,13905988122027295313489800,
%U A384022 76896867190774672671251191752,521595538342870729288480053506382,4258687803431080424982372253063299050,41202042785933045982333959380025893914894
%N A384022 a(n) = [x^(2*n)] Product_{k=0..n} 1/(1 - k*x)^3.
%F A384022 a(n) = Sum_{i, j, k>=0 and i+j+k=2*n} Stirling2(i+n,n) * Stirling2(j+n,n) * Stirling2(k+n,n).
%F A384022 a(n) ~ 5^(5*n + 1) * n^(2*n - 1/2) / (sqrt(2*Pi*(1-w)) * 3^(3*n + 3/2) * exp(2*n) * (5-3*w)^(2*n) * w^(3*n+1)), where w = -LambertW(-5*exp(-5/3)/3) = 0.5404054440316473268672191331988... - _Vaclav Kotesovec_, May 22 2025
%t A384022 Table[SeriesCoefficient[Product[1/(1-k*x)^3, {k, 1, n}], {x, 0, 2*n}], {n, 0, 15}] (* _Vaclav Kotesovec_, May 18 2025 *)
%t A384022 (* or *)
%t A384022 Table[Sum[StirlingS2[i+n, n] * StirlingS2[j+n, n] * StirlingS2[3*n-i-j, n], {i, 0, 2*n}, {j, 0, 2*n-i}], {n, 0, 15}] (* _Vaclav Kotesovec_, May 22 2025 *)
%o A384022 (PARI) a(n) = sum(i=0, 2*n, sum(j=0, 2*n-i, stirling(i+n, n, 2)*stirling(j+n, n, 2)*stirling(3*n-i-j, n, 2)));
%Y A384022 Cf. A383862.
%K A384022 nonn
%O A384022 0,2
%A A384022 _Seiichi Manyama_, May 17 2025