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%I #15 Jun 25 2022 07:37:08
%S 1,1,1,-1,-19,-153,-1155,-9785,-183075,-25013497,-11301739395,
%T -10911778097209,-21604455470794723,-86776403662147521913,
%U -702894028759616525605187,-11441974451382622345470900921,-373552937787342469475481963377571
%N E.g.f. A(x) satisfies A'(x) = 1 + A(2 * (1 - exp(-x)))/2.
%H Seiichi Manyama, <a href="/A355217/b355217.txt">Table of n, a(n) for n = 1..83</a>
%F a(1) = 1; a(n+1) = Sum_{k=1..n} (-1)^(n-k) * 2^(k-1) * 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-1)*stirling(i, j, 2)*v[j])); v;
%Y Cf. A355123, A355211.
%K sign
%O 1,5
%A _Seiichi Manyama_, Jun 24 2022
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