%I #14 Nov 10 2023 09:32:46

%S 1,1,3,19,187,2491,41951,855387,20491395,564179371,17555839639,

%T 609337562923,23340215770235,978038556122811,44506423393073487,

%U 2185725954288076987,115224508775345033779,6490005347933921581195,388973650645651854960455

%N E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^2) - 1)/A(x).

%H Seiichi Manyama, <a href="/A367180/b367180.txt">Table of n, a(n) for n = 0..372</a>

%F a(n) = Sum_{k=0..n} (2*n-k)!/(2*n-2*k+1)! * Stirling2(n,k).

%o (PARI) a(n) = sum(k=0, n, (2*n-k)!/(2*n-2*k+1)!*stirling(n, k, 2));

%Y Cf. A000272, A367181.

%Y Cf. A365438, A366729.

%Y Cf. A349601.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 08 2023