%I #13 Jun 25 2022 07:12:56

%S 1,1,1,0,-8,-64,-600,-14104,-1170120,-248815984,-115219852880,

%T -111345726833056,-220485042541083808,-885633596688107274496,

%U -7173767949430448755993856,-116777715174661360994951467008,-3812515511649504447203183936705536

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

%H Seiichi Manyama, <a href="/A355214/b355214.txt">Table of n, a(n) for n = 1..83</a>

%F a(1) = 1; a(n+1) = Sum_{k=1..n} 2^(k-1) * Stirling1(n,k) * a(k).

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

%Y Cf. A355120, A355208.

%K sign

%O 1,5

%A _Seiichi Manyama_, Jun 24 2022