A392566 - OEIS

%I #49 Mar 04 2026 09:52:19

%S 1,3,29,504,12885,438048,18648273,955478016,57293930313,3938025600000,

%T 305336853105669,26369255495467008,2510493688261968669,

%U 261252072029313662976,29504344983796139765625,3594050725647273953329152,469749733096169195471535633,65575342339459194563110895616

%N Expansion of e.g.f. (1/x) * Series_Reversion( x*exp(-x*(3+x)) ).

%F E.g.f. A(x) satisfies A(x) = exp(3*x*A(x) + (x*A(x))^2).

%F a(n) = n! * Sum_{k=0..floor(n/2)} (n+1)^(n-k-1) * 3^(n-2*k) * binomial(n-k,k)/(n-k)!.

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*exp(-x*(3+x)))/x))

%Y Cf. A088695, A120590, A192949.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 04 2026