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A380772 E.g.f. A(x) satisfies A(x) = exp(x * (1 + x*A(x)^2)) * (1 + x*A(x)^2).

%I A380772 #10 Feb 03 2025 11:07:32
%S A380772 1,2,13,166,3157,80466,2578969,99734230,4521335081,235215564706,
%T A380772 13815024321061,904313739020550,65287579679979133,5153929267246018546,
%U A380772 441668985219603417137,40834603462763102240566,4051601326622081640558673,429423186979619018132841282
%N A380772 E.g.f. A(x) satisfies A(x) = exp(x * (1 + x*A(x)^2)) * (1 + x*A(x)^2).
%F A380772 a(n) = n! * Sum_{k=0..n} (2*n-2*k+1)^(k-1) * binomial(2*n-k+1,n-k)/k!.
%o A380772 (PARI) a(n, q=1, r=2, s=0, t=1, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);
%Y A380772 Cf. A380769.
%K A380772 nonn
%O A380772 0,2
%A A380772 _Seiichi Manyama_, Feb 02 2025