OFFSET
1,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..200
FORMULA
Given g.f. A(x), then G(x) = d/dx A(x^3)/3 = Sum_{n>=1} n*a(n)*x^(3*n-1) is the g.f. of A212392 and satisfies: G(x) = (x + G(G(x)))^2.
G.f. satisfies: A’(x) = ( 1 + x*A’(x)^2 * A’(x^2*A’(x)^3) )^2 where A'(x) = d/dx A(x).
EXAMPLE
G.f.: A(x) = x + x^2 + 3*x^3 + 14*x^4 + 80*x^5 + 516*x^6 + 3608*x^7 + 26729*x^8 +...
Let G(x) = d/dx A(x^3)/3, then G(x) = (x + G(G(x)))^2, where
G(x) = x^2 + 2*x^5 + 9*x^8 + 56*x^11 + 400*x^14 + 3096*x^17 + 25256*x^20 +...
G(G(x)) = x^4 + 4*x^7 + 24*x^10 + 168*x^13 + 1284*x^16 + 10384*x^19 +...
PROG
(PARI) {a(n)=local(G=x^2+x^3); for(i=1, n, G=(x+subst(G, x, G+O(x^(3*n))))^2); polcoeff(G, 3*n-1)/n}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 12 2012
STATUS
approved