A367165 - OEIS

%I #11 Nov 07 2023 08:23:37

%S 1,1,5,52,835,18216,503349,16855084,663482831,30028551760,

%T 1536446339593,87704127028068,5525854843477995,380920533712670056,

%U 28518416931490444157,2304386381189483726044,199888539403801152219271,18526504345764539763792576

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

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

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

%Y Cf. A367166.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 07 2023