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 A371063 #30 Mar 10 2024 08:13:43
%S A371063 1,0,1,3,6,40,375,2541,21028,264636,3303765,41219695,625493946,
%T A371063 10676900598,185753808331,3495429297465,72963017028840,
%U A371063 1606964677740376,37107535997019753,918150959889615771,24110308315512081550,662150320109499176130,19105058680403510485671
%N A371063 E.g.f. satisfies A(x) = 1 + x^2/2*exp(x*A(x)).
%F A371063 a(n) = n! * Sum_{k=0..floor(n/2)} k^(n-2*k) * binomial(n-2*k+1,k)/( 2^k*(n-2*k+1)*(n-2*k)! ).
%t A371063 nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^3/2]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 10 2024 *)
%o A371063 (PARI) a(n) = n!*sum(k=0, n\2, k^(n-2*k)*binomial(n-2*k+1, k)/(2^k*(n-2*k+1)*(n-2*k)!));
%Y A371063 Cf. A161631, A371066.
%Y A371063 Cf. A371042.
%K A371063 nonn
%O A371063 0,4
%A A371063 _Seiichi Manyama_, Mar 09 2024