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 A373757 #17 Dec 30 2024 12:25:49
%S A373757 1,0,0,1,8,60,490,4480,45920,524440,6619200,91568400,1377884200,
%T A373757 22401579200,391192401600,7300174281400,144938169376000,
%U A373757 3049711320656000,67777255079934400,1586172656920051200,38984454900431040000,1003827897443395024000
%N A373757 Expansion of e.g.f. exp(x^3/(6 * (1 - x)^2)).
%F A373757 a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-k-1,n-3*k)/(6^k * k!).
%F A373757 a(0) = 1; a(n) = ((n-1)!/6) * Sum_{k=3..n} k * (k-2) * a(n-k)/(n-k)!.
%t A373757 With[{nn=30},CoefficientList[Series[Exp[x^3/(6(1-x)^2)],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Dec 30 2024 *)
%o A373757 (PARI) a(n) = n!*sum(k=0, n\3, binomial(n-k-1, n-3*k)/(6^k*k!));
%o A373757 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/6*sum(j=3, i, j*(j-2)*v[i-j+1]/(i-j)!)); v;
%Y A373757 Cf. A361533, A361573.
%K A373757 nonn
%O A373757 0,5
%A A373757 _Seiichi Manyama_, Jun 17 2024