OFFSET
0,3
FORMULA
G.f. A(x) = G(x)^2/x where G(x) is g.f. of A107096.
a(n)=T(n,1), T(n,m)=sum(i=1..n-m, binomial(2*m,i)*T(n-i,m))-sum(k=m+1..n-1, T(n,k)*T(k,m)), n>m, T(n,n)=1. [Vladimir Kruchinin May 03 2012]
PROG
(PARI) {a(n)=local(A, B, F); if(n<1, 0, F=x+2*x^2+x*O(x^n); A=F; for(j=0, n, for(i=0, j, B=serreverse(A); A=(A+subst(B, x, A*(1+x)^2))/2); A=round(A)); polcoeff(A, n, x))}
(Maxima) T(n, m):=if n=m then 1 else sum(binomial(2*m, i)*T(n-i, m), i, 1, n-m)-sum(T(n, k)*T(k, m), k, m+1, n-1); makelist(T(n, 1), n, 1, 10); [Vladimir Kruchinin May 03 2012]
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, May 12 2005
STATUS
approved