OFFSET
1,2
FORMULA
Functions C(x) and S(x) satisfy: C'(C(x))*C'(x) - S'(S(x))*S'(x) = 1.
EXAMPLE
G.f. S(x) = 2*x^2 + 16*x^5 + 192*x^8 + 3456*x^11 + 101376*x^14 +...
Related expansions.
C(x) = x + 4*x^4 + 32*x^7 + 384*x^10 + 6912*x^13 + 202752*x^16 +...
C(C(x)) = x + 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...
S(S(x)) = 8*x^4 + 128*x^7 + 2560*x^10 + 60416*x^13 + 1728512*x^16 +...
PROG
(PARI) {a(n)=local(C=x, S=2*x^2, Sv=[0, 2]);
for(i=0, n\3, Sv=concat(Sv, [0, 0, 0]); S=x*Ser(Sv); C=x+2*x^2*S;
Sv[#Sv]=polcoeff((subst(C, x, C)-subst(S, x, S))/4, #Sv+2); ); polcoeff(S, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 01 2011
STATUS
approved