%I #14 Mar 18 2024 12:00:55

%S 1,0,0,6,12,40,1620,13608,117600,2924640,49603680,782147520,

%T 19083936960,463369645440,10836652514688,304533583200000,

%U 9218842256332800,281872333420554240,9421579421176089600,338543319734116116480,12590519274541116518400

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

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

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

%Y Cf. A370994, A371118, A371138.

%Y Cf. A351503.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 18 2024