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 A383221 #12 May 06 2025 09:31:46
%S A383221 0,0,0,1,26,595,14155,363944,10206700,312193524,10380710220,
%T A383221 373619597736,14490750497432,603032132116336,26818416624389936,
%U A383221 1269883590624201344,63806666669904903808,3391580011320726010880,190174443042558311293440,11220246602286014617751040
%N A383221 Coefficient of x^3 in expansion of (x+2) * (x+5) * ... * (x+3*n-1).
%F A383221 a(n) = Sum_{k=3..n} 2^(k-3) * 3^(n-k) * binomial(k,3) * |Stirling1(n,k)|.
%F A383221 E.g.f.: f(x)^2 * log(f(x))^3 / 6, where f(x) = 1/(1 - 3*x)^(1/3).
%F A383221 a(n) = Sum_{k=3..n} (3*n-1)^(k-3) * 3^(n-k) * binomial(k,3) * Stirling1(n,k). - _Seiichi Manyama_, May 06 2025
%o A383221 (PARI) a(n) = polcoef(prod(k=0, n-1, x+3*k+2), 3);
%Y A383221 Column k=3 of A225470.
%K A383221 nonn
%O A383221 0,5
%A A383221 _Seiichi Manyama_, Apr 20 2025