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A213335
G.f. satisfies: A(x) = 1 + x/A(-x)^4.
8
1, 1, 4, -6, -84, 171, 2940, -6576, -124260, 291321, 5810120, -14012244, -289392508, 711239741, 15052561056, -37498302048, -808073773572, 2033589755205, 44436219882252, -112715767473482, -2490257138332712, 6356863001632326, 141706826771491368
OFFSET
0,3
LINKS
FORMULA
G.f. satisfies: A(x) = G(x/A(x)^4) where G(x) = A(x*G(x)^4) is the g.f. of A213336.
G.f. satisfies: A(x) = ( x/Series_Reversion( x*F(x/(1-x)^4)^4 ) )^(1/4) where F(x) = 1 + x*F(x)^4 is the g.f. of A002293.
G.f. satisfies: A(x) = A(x)*A(-x) + x/A(x)^3.
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