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 A382032 #17 Mar 14 2025 08:59:13
%S A382032 1,1,5,55,937,21741,639841,22839139,958882289,46304377849,
%T A382032 2528571710881,154076164781991,10364272238514217,762867688235619877,
%U A382032 60989719558159065857,5263030218009265964011,487578723768665716788961,48266847740986728218648433,5084697384633390178057209793
%N A382032 E.g.f. A(x) satisfies A(x) = exp(x*C(x*A(x))^2), where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.
%F A382032 a(n) = (n-1)! * Sum_{k=0..n-1} (k+1)^(n-k-1) * binomial(2*n,k)/(n-k-1)! for n > 0.
%F A382032 Let F(x) be the e.g.f. of A377553. F(x) = log(A(x))/x = C(x*A(x))^2.
%F A382032 E.g.f.: A(x) = exp( Series_Reversion( x/(1 + x*exp(x))^2 ) ).
%o A382032 (PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (k+1)^(n-k-1)*binomial(2*n, k)/(n-k-1)!));
%Y A382032 Cf. A161630, A382033, A382034.
%Y A382032 Cf. A000108, A377553, A382036.
%K A382032 nonn
%O A382032 0,3
%A A382032 _Seiichi Manyama_, Mar 12 2025