A209625 - OEIS

%I #6 Mar 31 2012 10:23:15

%S 1,2,6,24,114,600,3372,19824,120422,749848,4760228,30688560,200338740,

%T 1321408656,8791205496,58912586784,397228820742,2692522813848,

%U 18333530047428,125325068538672,859639878194844

%N G.f. A(x) satisfies A(A(x)-2*A(x)^2)=x/(1-2*x)

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

%o (Maxima)

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

%o makelist(T(n,1),n,1,7);

%K nonn

%O 1,2

%A _Vladimir Kruchinin_, Mar 11 2012