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

%I #8 Mar 16 2024 11:57:11

%S 1,0,0,6,12,40,1620,16128,154560,3378240,67828320,1247843520,

%T 28996704000,773215822080,20900234234880,609432997219200,

%U 19677823129036800,674330219708221440,24327437969162280960,936555233579552563200,38250260222888409292800

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

%F a(n) = n! * Sum_{k=0..floor(n/3)} (2*n-4*k)! * |Stirling1(n-2*k,k)|/( (n-2*k)! * (2*n-5*k+1)! ).

%o (PARI) a(n) = n!*sum(k=0, n\3, (2*n-4*k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(2*n-5*k+1)!));

%Y Cf. A371234, A371235.

%Y Cf. A371118.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 15 2024