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 A371319 #9 Mar 19 2024 08:37:46
%S A371319 1,1,3,13,97,881,10561,147505,2453025,46234081,988356961,23439248801,
%T A371319 613770379729,17541180307249,544252239627825,18203134190836561,
%U A371319 653255126565875521,25031281492493722817,1020214630056827123137,44067538801695759773761
%N A371319 E.g.f. satisfies A(x) = exp(x) + x^2*A(x)^2.
%F A371319 E.g.f.: 2*exp(x)/(1 + sqrt(1 - 4*x^2*exp(x))).
%F A371319 a(n) = n! * Sum_{k=0..floor(n/2)} (k+1)^(n-2*k-1) * binomial(2*k,k)/(n-2*k)!.
%o A371319 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(2*exp(x)/(1+sqrt(1-4*x^2*exp(x)))))
%o A371319 (PARI) a(n) = n!*sum(k=0, n\2, (k+1)^(n-2*k-1)*binomial(2*k, k)/(n-2*k)!);
%Y A371319 Cf. A087208, A371320.
%K A371319 nonn
%O A371319 0,3
%A A371319 _Seiichi Manyama_, Mar 18 2024