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 A382925 #41 May 22 2025 14:18:33
%S A382925 1,4,248,61320,39194896,51699564000,122482878310656,
%T A382925 474300956527856640,2804126507444905046272,24036712401508315774848000,
%U A382925 286889291626307627568309995520,4615084616716397442547883972818944,97421519516367186622078306709619806208
%N A382925 a(n) = [x^(3*n)] Product_{k=0..n} (1 + k*x)^4.
%F A382925 a(n) = Sum_{i, j, k, l>=0 and i+j+k+l=n} |Stirling1(n+1,i+1) * Stirling1(n+1,j+1) * Stirling1(n+1,k+1) * Stirling1(n+1,l+1)|.
%F A382925 a(n) ~ 2^(8*n + 7/2) * w^(4*n + 5/2) * n^(3*n - 1/2) / (sqrt(Pi*(w-1)) * exp(3*n) * (4*w-1)^(3*n)), where w = -LambertW(-1, -exp(-1/4)/4) = 2.5866629822630538811828... - _Vaclav Kotesovec_, May 22 2025
%t A382925 Abs[Table[Sum[StirlingS1[n+1, i+1] * StirlingS1[n+1, j+1] * StirlingS1[n+1, k+1] * StirlingS1[n+1, n-i-j-k+1], {i, 0, n}, {j, 0, n-i}, {k, 0, n-i-j}], {n, 0, 15}]] (* _Vaclav Kotesovec_, May 22 2025 *)
%o A382925 (PARI) a(n) = sum(i=0, n, sum(j=0, n-i, sum(k=0, n-i-j, abs(stirling(n+1, i+1, 1)*stirling(n+1, j+1, 1)*stirling(n+1, k+1, 1)*stirling(n+1, n-i-j-k+1, 1)))));
%Y A382925 Cf. A129256, A384025.
%Y A382925 Cf. A384031, A384032.
%K A382925 nonn
%O A382925 0,2
%A A382925 _Seiichi Manyama_, May 17 2025