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%I #8 Jun 20 2022 08:36:04
%S 1,1,4,54,1928,167770,34128972,15867798142,16621680303888,
%T 38813463431274402,200266228576991017940,2265670919773168963168454,
%U 55816752493202168837392763544,2976116188645489878229876218205674,341574630434025162744892242114482410332
%N E.g.f. A(x) satisfies A(x) = 1 + x * A(2 * (exp(x) - 1)).
%F a(0) = 1; a(n) = n * Sum_{k=0..n-1} 2^k * Stirling2(n-1,k) * a(k).
%F a(n) = n * A355131(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*stirling(i-1, j, 2)*v[j+1])); v;
%Y Cf. A048801, A355100, A355131.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 20 2022
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