OFFSET
0,3
FORMULA
EXAMPLE
G.f: 1 + 6*x^2 + 28*x^3 + 2684*x^4 + 85664*x^5 + 96848424*x^6 +...
which equals sqrt( C(x)^2 - S(x)^2 ) where
C(x) = 1 + 8*x^2 + 32*x^3 + 2848*x^4 + 87808*x^5 + 97425920*x^6 +...
S(x) = 2*x + 2*x^2 + 88*x^3 + 1028*x^4 + 289184*x^5 + 22451552*x^6 +...
Related expansions:
C(x) + S(x) = 1 + 2*x + 10*x^2 + 120*x^3 + 3876*x^4 + 376992*x^5 +...
C(x) - S(x) = 1 - 2*x + 6*x^2 - 56*x^3 + 1820*x^4 - 201376*x^5 +...
PROG
(PARI) {a(n)=polcoeff(sqrt(sum(k=0, n, log(1-2^(2*k)*x +x*O(x^n))^(2*k)/(2*k)!)^2-sum(k=0, n, log(1-2^(2*k+1)*x +x*O(x^n))^(2*k+1)/(2*k+1)!)^2), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 22 2009
STATUS
approved