%I #9 Jun 18 2022 23:03:47

%S 1,1,3,32,962,74604,14102416,6268777248,6394217598800,

%T 14703540690658848,75208658403123879744,846736815151560907880448,

%U 20804324374762392749905814784,1107653447201119751335031683041792,127026805293926861783650032004892737536

%N E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(2*x).

%F a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k-1) * 2^(n-k) * (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]=sum(j=1, i, (-1)^(j-1)*2^(i-j)*(j-1)!*binomial(i, j)*v[i-j+1])); v;

%Y Cf. A006252, A355085.

%Y Cf. A352860, A355086.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 18 2022