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A143597
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G.f. satisfies: A(x) = 1 + x*A(2x)*A(-x).
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0
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1, 1, 1, 3, 19, 297, 8953, 572155, 72116459, 18460128753, 9414877745601, 9640779710687955, 19725063387945457219, 80793830752052788593529, 661701532957780822275151305, 10841317673677535233876159099755
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| G.f. satisfies: A(x) = (1 + x*A(2x))/(1 + x^2*A(2x)*A(-2x)).
a(n) = Sum_{k=0..n-1} 2^k*(-1)^(n-1-k)*a(k)*a(n-1-k) for n>0 with a(0)=1.
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EXAMPLE
| G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 19*x^4 + 297*x^5 + 8953*x^6 +...
A(x) = 1 + x*A(2x)*[1 - x*A(-2x)*[1 + x*A(2x)*[1 - x*A(-2x)*[1 +...]]]].
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PROG
| (PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)*subst(A, x, -x)); polcoeff(A, n)}
(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, 2^k*(-1)^(n-1-k)*a(k)*a(n-1-k)))}
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CROSSREFS
| Sequence in context: A069344 A173799 A003011 * A115705 A136171 A102586
Adjacent sequences: A143594 A143595 A143596 * A143598 A143599 A143600
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 28 2008
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