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 A383222 #12 May 06 2025 09:31:50
%S A383222 0,0,0,0,1,40,1275,39655,1276009,43382934,1570298610,60630265740,
%T A383222 2495678898636,109326548645600,5085420626585936,250576924194171120,
%U A383222 13046999027750243984,716156618057417103008,41347880768363832470304,2505655766070932929630464
%N A383222 Coefficient of x^4 in expansion of (x+2) * (x+5) * ... * (x+3*n-1).
%F A383222 a(n) = Sum_{k=4..n} 2^(k-4) * 3^(n-k) * binomial(k,4) * |Stirling1(n,k)|.
%F A383222 E.g.f.: f(x)^2 * log(f(x))^4 / 24, where f(x) = 1/(1 - 3*x)^(1/3).
%F A383222 a(n) = Sum_{k=4..n} (3*n-1)^(k-4) * 3^(n-k) * binomial(k,4) * Stirling1(n,k). - _Seiichi Manyama_, May 06 2025
%o A383222 (PARI) a(n) = polcoef(prod(k=0, n-1, x+3*k+2), 4);
%o A383222 (PARI) first(n) = {my(res = vector(n), v = [1, 0, 0, 0, 0], cv, c = -1, pc = 1); for(i = 2, n, c+=3; pc *= c; cv = v[^5]; cv = concat(0, cv); cv+=v*c; v = cv; res[i] = v[5]); res} \\ _David A. Corneth_, May 06 2025
%Y A383222 Column k=4 of A225470.
%K A383222 nonn,easy
%O A383222 0,6
%A A383222 _Seiichi Manyama_, Apr 20 2025