OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..100
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
where
1/A(-x) = 1 + x - 2*x^2 - 8*x^3 + 30*x^4 + 143*x^5 - 638*x^6 - 3272*x^7 +...
x/A(-x)^3 = x + 3*x^2 - 3*x^3 - 35*x^4 + 48*x^5 + 693*x^6 - 1046*x^7 +...
A(x)^3 = 1 + 3*x + 12*x^2 + 10*x^3 - 87*x^4 - 102*x^5 + 1632*x^6 + 1974*x^7 +...
The g.f. G(x) of A213282 begins:
G(x) = 1 + x + 6*x^2 + 36*x^3 + 236*x^4 + 1656*x^5 + 12192*x^6 + 92960*x^7 +...
where G(x) = A(x*G(x)^3) and G(x/A(x)^3) = A(x);
also, G(x) = F(x/(1-x)^3) where F(x) = 1 + x*F(x)^3 is g.f. of A001764:
G(x) = 1 + x + 3*x^2 + 12*x^3 + 55*x^4 + 273*x^5 + 1428*x^6 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x/subst(A^3, x, -x+x*O(x^n))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 08 2012
STATUS
approved