%I #17 Mar 12 2022 11:15:42

%S 1,1,3,19,123,1021,10683,127093,1725867,26535613,452307243,8475606613,

%T 173390108235,3842119808749,91675559886459,2343875745873493,

%U 63920729617231275,1852126733351677021,56823327291638414667,1840195730889731550805

%N Expansion of e.g.f. 1/(2 - exp(x) - x^3).

%F a(n) = n * (n-1) * (n-2) * a(n-3) + Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.

%t m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x^3), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x^3)))

%o (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));

%o a(n) = b(n, 3);

%Y Cf. A006155, A346269, A352300.

%Y Cf. A352303, A352307.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 11 2022