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A213225
G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^4)).
8
1, 1, 2, 6, 20, 76, 313, 1375, 6337, 30243, 148129, 739172, 3737993, 19077868, 97955307, 504707999, 2604312205, 13436676965, 69229324721, 355854322633, 1823672937884, 9314227843463, 47406130512872, 240498260267049, 1216833204738419, 6146116088495029
OFFSET
0,3
COMMENTS
Compare g.f. to:
(1) G(x) = 1/(1 - x/G(-x*G(x)^3)^1) when G(x) = 1/(1 - x*G(x)^1) (A000108).
(2) G(x) = 1/(1 - x/G(-x*G(x)^5)^2) when G(x) = 1/(1 - x*G(x)^2) (A001764).
(3) G(x) = 1/(1 - x/G(-x*G(x)^7)^3) when G(x) = 1/(1 - x*G(x)^3) (A002293).
(4) G(x) = 1/(1 - x/G(-x*G(x)^9)^4) when G(x) = 1/(1 - x*G(x)^4) (A002294).
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 20*x^4 + 76*x^5 + 313*x^6 +...
Related expansions:
A(x)^4 = 1 + 4*x + 14*x^2 + 52*x^3 + 201*x^4 + 816*x^5 + 3468*x^6 +...
1/A(-x*A(x)^4) = 1 + x + 3*x^2 + 9*x^3 + 35*x^4 + 146*x^5 + 656*x^6 +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A, x, -x*subst(A^4, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 06 2012
STATUS
approved