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%I #14 Jun 25 2022 07:37:21
%S 1,2,6,26,182,2746,111350,11245882,2521162358,1193350247226,
%T 1165982253097718,2322179762944209722,9356100009656750248822,
%U 75909020176742648718140218,1236750544861403327611377577974,40395601774769639548336167153191738
%N E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (1 - exp(-x))).
%H Seiichi Manyama, <a href="/A355211/b355211.txt">Table of n, a(n) for n = 1..82</a>
%F a(1) = 1; a(n+1) = Sum_{k=1..n} (-1)^(n-k) * 2^k * Stirling2(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, (-1)^(i-j)*2^j*stirling(i, j, 2)*v[j])); v;
%Y Cf. A355132, A355203, A355207.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Jun 24 2022
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