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 A351507 #21 May 19 2025 04:32:14
%S A351507 1,1,13,630,65446,11732175,3222746276,1257489289280,661150527657180,
%T A351507 450529025613124095,386183537239831846450,406654820487854059966416,
%U A351507 516014868401631381045209376,776565429016998902169538130936,1367544537916924083498367095477800
%N A351507 a(n) = [x^n] Product_{k=1..n} (1 + k*x)^n.
%F A351507 a(n) ~ exp(n + 1/3) * n^(2*n - 1/2) / (sqrt(Pi) * 2^(n + 1/2)). - _Vaclav Kotesovec_, Feb 18 2022
%F A351507 a(n) = Sum_{0 <= x_1, x_2,..., x_n <= n and x_1 + x_2 + ... + x_n = (n-1)*n} Product_{k=1..n} |Stirling1(n + 1,x_k + 1)|. - _Seiichi Manyama_, May 18 2025
%t A351507 Table[SeriesCoefficient[Product[(1 + k*x)^n, {k,1,n}], {x,0,n}], {n,0,20}] (* _Vaclav Kotesovec_, Feb 18 2022 *)
%o A351507 (PARI) a(n) = polcoef(prod(k=1, n, 1+k*x)^n, n);
%Y A351507 Cf. A000142, A129256, A384012, A384031.
%Y A351507 Cf. A351508, A384017.
%K A351507 nonn
%O A351507 0,3
%A A351507 _Seiichi Manyama_, Feb 12 2022