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E.g.f. satisfies A(x) = 1 + x*A(x)^2 * (exp(x*A(x)^2) - 1).
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%I #9 Mar 17 2024 04:06:47

%S 1,0,2,3,100,605,18366,238147,7688584,162016857,5839673410,

%T 172051422191,7034104918380,265080848463301,12311587474831750,

%U 561485310426413115,29475848282815342096,1569372890780660724401,92402629467727290784650

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

%F a(n) = n! * (2*n)! * Sum_{k=0..floor(n/2)} Stirling2(n-k,k)/( (n-k)! * (2*n-k+1)! ).

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

%Y Cf. A371262, A371269, A371271.

%Y Cf. A371229.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 16 2024