%I #12 Mar 10 2022 10:54:37

%S 1,2,8,51,427,4485,56461,829619,13929175,263120293,5522411441,

%T 127497249825,3211140897757,87615489275587,2574463431688695,

%U 81050546853002151,2721785052811891411,97113737702073060713,3668859532725782696709,146306156466305491481253

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

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

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

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

%Y Cf. A000670, A007840, A352147, A352270.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 10 2022