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E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^2).
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%I #8 Mar 16 2024 11:57:32

%S 1,0,2,3,56,390,6384,92400,1812768,38565072,949927680,25934040000,

%T 783458550720,25909868761920,930720395219328,36108805836317760,

%U 1504050682102456320,66964478742976711680,3173178938051223889920,159461567895099436047360

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

%F a(n) = n! * Sum_{k=0..floor(n/2)} (2*n-2*k)! * |Stirling1(n-k,k)|/( (n-k)! * (2*n-3*k+1)! ).

%o (PARI) a(n) = n!*sum(k=0, n\2, (2*n-2*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(2*n-3*k+1)!));

%Y Cf. A371228, A371229, A371230.

%Y Cf. A371117.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 15 2024