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 A373741 #10 Apr 26 2025 11:33:11
%S A373741 1,0,1,9,39,150,1365,13545,105945,918540,10603845,127806525,
%T A373741 1468823895,18253765530,257397445305,3770163121725,55637459903025,
%U A373741 866703333295800,14468243658093225,250223925107581425,4426399346291497575,81488489549760042750
%N A373741 Expansion of e.g.f. exp(x^2/2 * (1 + x)^3).
%F A373741 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*k,n-2*k)/(2^k * k!).
%F A373741 a(n) = (n-1)/2 * (2*a(n-2) + 9*(n-2)*a(n-3) + 12*(n-2)*(n-3)*a(n-4) + 5*(n-2)*(n-3)*(n-4)*a(n-5)).
%t A373741 With[{nn=30},CoefficientList[Series[Exp[x^2/2 (1+x)^3],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 26 2025 *)
%o A373741 (PARI) a(n) = n!*sum(k=0, n\2, binomial(3*k, n-2*k)/(2^k*k!));
%Y A373741 Cf. A361567, A373740.
%Y A373741 Cf. A116090.
%K A373741 nonn
%O A373741 0,4
%A A373741 _Seiichi Manyama_, Jun 16 2024