OFFSET
0,2
EXAMPLE
G.f.: A(x) = 1 + 4*x + 25*x^2 + 144*x^3 + 1024*x^4 + 7396*x^5 +...
Describe the g.f. of A173610 by:
B(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 25*x^5 + 60*x^6 + 144*x^7 +...
then the g.f. of A173611 is given by C(x) = B(x)^2:
C(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 32*x^4 + 86*x^5 +...
where the square of the coefficients of C(x) form this sequence
and yields the odd bisection of A173610.
PROG
(PARI) {a(n)=local(A=1+x, B); for(i=1, n, B=(A+x*O(x^n))^2; A=1+x*sum(m=0, n\2, polcoeff(B, m)*polcoeff(B, m+1)*x^(2*m+1)) +x*sum(m=0, n\2, polcoeff(B, m)^2*x^(2*m))); polcoeff(A^2, n)^2}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 22 2010
STATUS
approved