A107095 G.f. satisfies: A(A(x)) = (1+x)^2*A(x).

0, 1, 2, -3, 18, -150, 1518, -17541, 223782, -3087948, 45470022, -707810715, 11569008816, -197540043324, 3509923686678, -64697804055675, 1234127209128306, -24312707152663590, 493834352052852738, -10327320248199824889, 222086739445484152590

Offset: 0

Author

Paul D. Hanna, May 12 2005

Keywords

• sign

Crossrefs

Cf. A107096.

Programs

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,0,10); /* Vladimir Kruchinin May 03 2012 */

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))}

Formula

G.f.: A(x) = G(x)^2/x where G(x) is g.f. of A107096.

a(n) = T(n,1), where 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]