OFFSET
1,2
FORMULA
EXAMPLE
G.f.: A(x) = x + 2*x^3 + 15*x^5 + 165*x^7 + 2213*x^9 + ...
A(x)^3 = x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + 145815*x^13 + ...
A(x) = G(G(x)) where
G(x) = x + x^3 + 6*x^5 + 57*x^7 + 683*x^9 + 9474*x^11 + ...
Also, A(x) = G(x) + G(G(G(x)))^3 where G(G(G(x))) begins
G(G(G(x))) = x + 3*x^3 + 27*x^5 + 339*x^7 + 5067*x^9 + 84738*x^11 + ... + A153853(n)*x^(2*n-1) + ...
G(G(G(x)))^3 = x^3 + 9*x^5 + 108*x^7 + 1530*x^9 + 24219*x^11 + ...
PROG
(PARI) {a(n)=local(G=x+O(x^(2*n+1))); for(i=0, n, G=serreverse(x-G^3)); polcoeff(subst(G, x, G), 2*n-1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 21 2009
EXTENSIONS
Formula corrected by Paul D. Hanna, Dec 07 2009
STATUS
approved