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%I #8 Sep 11 2022 10:07:10
%S 1,0,1,3,16,135,1246,14238,192613,2948025,51071236,985911003,
%T 20952667660,486857940660,12275673296251,333786662478363,
%U 9737819506544272,303399477464036175,10054949172135522106,353197317869395005258,13108298181041284002769
%N E.g.f. satisfies A(x) * log(A(x)) = (exp(x*A(x)) - 1)^2 / 2.
%F a(n) = Sum_{k=0..floor(n/2)} (2*k)! * (n-k+1)^(k-1) * Stirling2(n,2*k)/(2^k * k!).
%o (PARI) a(n) = sum(k=0, n\2, (2*k)!*(n-k+1)^(k-1)*stirling(n, 2*k, 2)/(2^k*k!));
%Y Cf. A349588, A357089.
%K nonn
%O 0,4
%A _Seiichi Manyama_, Sep 11 2022
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