OFFSET
0,3
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 26*x^4 + 127*x^5 + 478*x^6 +...
Compare bisections of A(x)^2, A(x)^2*A(-x), and A(x)^4*A(-x)^2:
A(x)^2 = 1 + 2*x + 5*x^2 + 20*x^3 + 72*x^4 + 338*x^5 + 1378*x^6 + 6952*x^7 +...
A(x)^2*A(-x) = 1 + x + 5*x^2 + 11*x^3 + 72*x^4 + 191*x^5 + 1378*x^6 + 3979*x^7 +...
A(x)^4*A(-x)^2 = 1 + 2*x + 11*x^2 + 32*x^3 + 191*x^4 + 636*x^5 + 3979*x^6 +...
Related expansions:
A(x)^3 = 1 + 3*x + 9*x^2 + 37*x^3 + 144*x^4 + 669*x^5 + 2882*x^6 + 14229*x^7 +...
A(x)^3*A(-x) = 1 + 2*x + 8*x^2 + 26*x^3 + 127*x^4 + 478*x^5 + 2536*x^6 +...
A(x)^3*A(-x)^2 = 1 + x + 8*x^2 + 14*x^3 + 127*x^4 + 264*x^5 + 2536*x^6 +...
PROG
(PARI) {a(n)=local(A=1+x+O(x^21)); for(i=0, n, A=1+x*A^3*subst(A, x, -x)); polcoeff(A, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 09 2008
STATUS
approved