OFFSET
0,3
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..100
FORMULA
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 - 6*x^3 - 84*x^4 + 171*x^5 + 2940*x^6 - 6576*x^7 +...
where
1/A(-x) = 1 + x - 3*x^2 - 13*x^3 + 77*x^4 + 402*x^5 - 2849*x^6 - 16040*x^7 +...
1/A(-x)^4 = 1 + 4*x - 6*x^2 - 84*x^3 + 171*x^4 + 2940*x^5 - 6576*x^6 +...
A(x)^4 = 1 + 4*x + 22*x^2 + 28*x^3 - 263*x^4 - 476*x^5 + 8740*x^6 +...
The g.f. G(x) of A213336 begins:
G(x) = 1 + x + 8*x^2 + 64*x^3 + 568*x^4 + 5440*x^5 + 54888*x^6 +...
where G(x) = A(x*G(x)^4) and G(x/A(x)^4) = A(x);
also, G(x) = F(x/(1-x)^4) where F(x) = 1 + x*F(x)^4 is g.f. of A002293:
F(x) = 1 + x + 4*x^2 + 22*x^3 + 140*x^4 + 969*x^5 + 7084*x^6 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x/subst(A^4, x, -x+x*O(x^n))); polcoeff(A, n)}
for(n=0, 40, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jun 09 2012
STATUS
approved