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 A375225 #10 Nov 20 2024 18:13:07
%S A375225 1,3,14,96,876,9780,127200,1877400,30947280,563114160,11202135840,
%T A375225 241655641920,5614182826560,139647350082240,3700648372861440,
%U A375225 104032358410780800,3090961262246457600,96747013002684844800,3180863885996673676800,109570715078766355814400
%N A375225 Expansion of e.g.f. exp( x^2/(1-x)^3 ) / (1-x)^3.
%F A375225 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(n+2+k,n-2*k)/k!.
%t A375225 With[{nn=20},CoefficientList[Series[Exp[x^2/(1-x)^3]/(1-x)^3,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 20 2024 *)
%o A375225 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x^2/(1-x)^3)/(1-x)^3))
%o A375225 (PARI) a(n) = n!*sum(k=0, n\2, binomial(n+2+k, n-2*k)/k!);
%Y A375225 Cf. A375172, A375224.
%Y A375225 Cf. A351767.
%K A375225 nonn
%O A375225 0,2
%A A375225 _Seiichi Manyama_, Aug 06 2024