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E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(log(1+x)).
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%I #13 Jun 04 2022 09:42:26

%S 1,1,1,-1,-6,39,97,-4481,33912,676236,-26413226,238849819,14313503696,

%T -755420105545,10108190752293,933595772081187,-74703766573019512,

%U 1828010869875477868,148132864489851652128,-19789393233722946227592,910780967051245532791008

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

%F E.g.f. A(x) satisfies: A(exp(x) - 1) = 1 + x*A(x).

%F a(0) = 1; a(n) = Sum_{k=1..n} k * Stirling1(n,k) * a(k-1).

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

%Y Cf. A135750, A213357, A354729.

%K sign

%O 0,5

%A _Seiichi Manyama_, Jun 04 2022