A201779 - OEIS

%I #5 Mar 31 2012 10:23:14

%S 1,1,2,5,11,23,52,120,247,534,1433,2540,3264,30169,19123,-363258,

%T 2951500,-1601367,-99325484,799655132,-1194225728,-32599353806,

%U 345568196667,-1063427879019,-13137091603516,205598895773140,-1103275663780401

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

%F a(n)=T(n,1), T(n,m)=sum(k=1..n-m, T(n-m,k)*sum(binomial(i+m-1,m-1)*binomial(i+m,k-i),i,0,k)-binomial(n-1,k+m-2)*T(k+m-1,m)), n>m, 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)*sum(binomial(i+m-1,m-1)*binomial(i+m,k-i),i,0,k)-binomial(n-1,k+m-2)*T(k+m-1,m),k,1,n-m)) else BB[n,m];

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

%K sign

%O 1,3

%A _Vladimir Kruchinin_, Dec 04 2011