%I #8 Feb 28 2022 14:24:56
%S 1,1,3,31,1393,330361,488337121,5197945772881,452395544496860161,
%T 360573039112103480718721,2914843277842193790386417088001,
%U 262261378512171017948642290003977004801,285983731923953608933716749772942709840131379201
%N G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^n/sf(n) where A(x) = Sum_{n>=0} a(n)*x^n/sf(n), and sf(n) = Product_{k=0..n} k! is the superfactorial of n (A000178).
%F G.f.: A(x) = (1/x)*Series_Reversion(x/F(x)) where F(x) = Sum_{n>=0} x^n/sf(n) and sf(n) = Product_{k=0..n} k!.
%e G.f.: A(x) = 1 + x + 3*x^2/(1!*2!) + 31*x^3/(1!*2!*3!) + 1393*x^4/(1!*2!*3!*4!) + 330361*x^5/(1!*2!*3!*4!*5!) + 488337121*x^6/(1!*2!*3!*4!*5!*6!) +...
%e where
%e A(x) = 1 + x*A(x) + x^2*A(x)^2/(1!*2!) + x^3*A(x)^3/(1!*2!*3!) + x^4*A(x)^4/(1!*2!*3!*4!) +...
%o (PARI) {a(n)=local(F=sum(m=0,n,x^m/prod(k=0,m,k!)+x*O(x^n)));prod(k=0,n,k!)*polcoeff(1/x*serreverse(x/F),n)}
%o (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(m=0,n,x^m*(A+x*O(x^n))^m/prod(k=0,m,k!)));prod(k=0,n,k!)*polcoeff(A,n)}
%Y Cf. A000178.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 05 2011
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