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A143564
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G.f. satisfies: A(x) = 1 + x*A(x)^4/A(-x)^3.
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1
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1, 1, 7, 31, 273, 1697, 16471, 116159, 1186081, 8928193, 94017703, 736522975, 7917810225, 63722594657, 695248655095, 5705316231551, 62944217175617, 524183926274433, 5833380674885959, 49141433498848159, 550674827214221137
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f. satisfies: A(x) + A(-x) = 1 + (1+x^2)*A(x)*A(-x).
G.f.: A(x) = G(x)/(1+x^2) where G(x) = 1 + x*G(x)^4/G(-x)^4 is the g.f. of A143557.
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EXAMPLE
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G.f. A(x) = 1 + x + 7*x^2 + 31*x^3 + 273*x^4 + 1697*x^5 +...
A(x)*A(-x) = 1 + 13*x^2 + 533*x^4 + 32409*x^6 + 2339753*x^8 +...
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PROG
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^4/subst(A^3, x, -x)); polcoeff(A, n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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