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E.g.f. satisfies: A(x+1/2*x^2)=x*exp(A(x)).
0

%I #7 Mar 31 2012 10:23:14

%S 1,1,3,7,30,96,343,4117,-7200,-117350,13210791,-301763373,352971853,

%T 347188696141,-18233731779780,353928253113421,23894270709259005,

%U -2906056754069734431,143316419628690145837,1110191131102178184400,-954513349352250528933834,97402126796076086688319561,-3777060544481584990339497402

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

%F a(n) = n!*T(n,1), T(n,m) = sum(k=1..n-m, T(n-m,k)*m^k/k! - 2^(k+m-n-1)*binomial(k+m-1,n-k-m+1)*T(k+m-1,m)), n>m, with T(n,n)=1.

%o (Maxima)

%o array(BB,100,100);

%o fillarray (BB, makelist (-1, i, 1, 1000));

%o T(n,m):=if BB[n,m]=-1 then BB[n,m]:(if n=m then 1 else sum(T(n-m,k)*m^k/k!-2^(k+m-n-1)*binomial(k+m-1,n-k-m+1)*T(k+m-1,m),k,1,n-m)) else BB[n,m];

%o makelist(n!*T(n,1),n,1,27);

%K sign

%O 1,3

%A _Vladimir Kruchinin_, Dec 05 2011