OFFSET
0,4
FORMULA
EXAMPLE
A(x) = 1 + x + x^2 + 4*x^3 + 9*x^4 + 25*x^5 + 64*x^6 + 256*x^7 +...
Take the square root of each term, a(n)^(1/2), and
let B(x) be the g.f. of the resulting sequence:
B(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 16*x^7 +...
Then 1/B(x) = 1 - x*A(x^2):
1/B(x) = 1 - x - x^3 - x^5 - 4*x^7 - 9*x^9 - 25*x^11 - 64*x^13 -...
PROG
(PARI) {a(n)=if(n==0, 1, sum(k=0, n\2, polcoeff(x^(n-2*k)*(sum(j=0, k, a(j)*x^(2*j))+x*O(x^n))^(n-2*k), n))^2)}
(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+x+O(x^2); while(m<=n, m*=2; A=1/(1-x*sum(k=0, m-1, polcoeff(A, k)^2*x^(2*k), O(x^(2*m))))); polcoeff(A, n)^2)} /* Michael Somos, Aug 18 2006 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 14 2006
STATUS
approved