A367851 - OEIS

%I #11 Dec 03 2023 01:43:44

%S 1,2,10,80,872,11984,198416,3840192,85031040,2119385856,58714881792,

%T 1789646610432,59515302478848,2144299161348096,83204666280609792,

%U 3459286210445942784,153413140701637804032,7228914528043587796992,360670654712328998289408

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

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

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*v[i]+sum(j=1, i, 2^(j-1)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A052820, A367852, A367853.

%Y Cf. A227917, A355110, A367845.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 02 2023