%I #8 Dec 30 2024 04:28:19

%S 1,1,11,158,3597,107994,4082695,186003166,9930511577,608225910290,

%T 42049314628251,3239451955702038,275220868466701861,

%U 25565354021529630970,2577774089234276245391,280406846696018760511694,32732658189778781519050161,4081497882738710247779141922

%N Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - 2*x*exp(x)) ).

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

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

%Y Cf. A379659, A379688.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 29 2024