OFFSET
1,1
FORMULA
G.f. A(x)=1-sqrt(1-4x+A(x^2)) satisfies A(x)^2-2A(x)+4x-A(x^2)=0, A(0)=0. - Michael Somos, Sep 06 2003
a(n)=(sum a(i)a(j), i+j=n, i<j)+(if n=2k, (a(k)-1)a(k)/2), n>1. a(1)=2.
MATHEMATICA
a[1] = 2; a[n_] := a[n] = Sum[a[k]*a[n-k], {k, 1, Floor[(n-1)/2]}] + If[EvenQ[n], (a[n/2]-1)*a[n/2]/2, 0]; Table[a[n], {n, 1, 28}] (* Jean-François Alcover, Feb 20 2012, from formula *)
PROG
(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=O(x); while(m<=n, m*=2; A=1-sqrt(1-4*x+subst(A, x, x^2))); polcoeff(A, n))
CROSSREFS
KEYWORD
easy,nonn,nice
AUTHOR
Claude Lenormand (claude.lenormand(AT)free.fr), Aug 29 2001
STATUS
approved