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E.g.f. A(x) satisfies: A(x) = 1 + x * A(-2 * log(1-x)).
1

%I #10 Jun 20 2022 08:36:31

%S 1,1,4,54,1936,168780,34360128,15979581632,16740281020160,

%T 39091514910283872,201702609432140369280,2281926772696486970224192,

%U 56217269029941735581289119232,2997472083791372184890466743907712,344025706673467887482938899075885442048

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

%F a(0) = 1; a(n) = n * Sum_{k=0..n-1} 2^k * |Stirling1(n-1,k)| * a(k).

%F a(n) = n * A355134(n-1) for n>0.

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i*sum(j=0, i-1, 2^j*abs(stirling(i-1, j, 1))*v[j+1])); v;

%Y Cf. A354730, A355106, A355134.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 20 2022