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A143550
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G.f. satisfies: A(x) = 1 + x*A(x)^4*A(-x)^2.
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5
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1, 1, 2, 11, 38, 257, 1040, 7646, 33374, 256718, 1171454, 9270560, 43558064, 351490167, 1686018600, 13799914556, 67223728270, 556203232266, 2741975026412, 22880729474777, 113875773363274, 956800135969601
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^6.
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EXAMPLE
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G.f. A(x) = 1 + x + 2*x^2 + 11*x^3 + 38*x^4 + 257*x^5 + 1040*x^6 +...
Related expansions:
A(x)^4 = 1 + 4*x + 14*x^2 + 72*x^3 + 333*x^4 + 1936*x^5 + 9966*x^6 +...
A(-x)^2 = 1 - 2*x + 5*x^2 - 26*x^3 + 102*x^4 - 634*x^5 + 2867*x^6 -+...
A(x)^2*A(-x) = 1 + x + 5*x^2 + 14*x^3 + 102*x^4 + 348*x^5 + 2867*x^6 +...
A(x)*A(-x) = 1 + 3*x^2 + 58*x^4 + 1597*x^6 + 51406*x^8 + 1807747*x^10 +...
[A(x)*A(-x)]^6 = 1 + 18*x^2 + 483*x^4 + 15342*x^6 + 535161*x^8 +...
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PROG
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(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, 2*n, A=1+x*A^4*subst(A^2, x, -x)); polcoeff(A, n)}
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CROSSREFS
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Cf. A143338, A143549, A143551, A143552, A143553, A143554.
Sequence in context: A196850 A203534 A166989 * A000175 A187259 A125064
Adjacent sequences: A143547 A143548 A143549 * A143551 A143552 A143553
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 24 2008
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STATUS
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approved
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