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%I #8 Mar 31 2012 10:23:14
%S 1,1,0,2,2,10,28,130,564,3102,17464,114282,784008,5987482,48279164,
%T 422742854,3909897740,38675519334,403121938616,4449327971330,
%U 51570742407808,628575203791026,8017017724008788,106974723312803902,1488628872502049348
%N E.g.f. A(x) satisfies A''(x)+A'(x)=exp(A(x))+1.
%o (Maxima)
%o Composita(n,k,F):=block([],if k=1 then F(n) else if n=k then (F(1))^n else sum(F(i+1)*Composita(n-i-1,k-1,F),i,0,n-k));
%o SolveDiff21(G,key):=block([b],array(b,100), b[1]:1, b[2]:1/2,bfun(n):=b[n], makelist(b[n]:-b[n-1]/n+1/(n*(n-1))*sum(Composita(n-2,k,bfun)*G(k) ,k,1,n-2),n,3,20),
%o if key=1 then makelist(n!*b[n],n,1,20) else makelist(b[n],n,1,20));
%o f(n):=1/n!;
%o SolveDiff21(f,1);
%K nonn
%O 1,4
%A _Vladimir Kruchinin_, Nov 25 2011
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