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A140092
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G.f. satisfies: A(x) = Series_Reversion[ x/sqrt(1 + 4*A(x)) ] with A(0)=0.
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1
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1, 2, 6, 28, 174, 1308, 11300, 108808, 1145078, 12996332, 157580252, 2026874424, 27507762028, 392226116696, 5855551243464, 91263899531280, 1481385005886374, 24989341719984972, 437270678940944556, 7923785627972483672
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OFFSET
| 1,2
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FORMULA
| G.f. satisfies: A(x) = x*sqrt(1 + 4*A(A(x))).
G.f. satisfies: A(A(x)) = [(A(x)^2 - x^2]/(2*x)^2.
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EXAMPLE
| G.f.: A(x) = x +2*x^2 +6*x^3 + 28*x^4 + 174*x^5 +1308*x^6 +11300*x^7 +...
A(A(x)) = x + 4*x^2 + 20*x^3 +124*x^4 + 912*x^5 +7676*x^6 +72064*x^7 +...
A(x)^2 = x^2 +4*x^3 + 16*x^4 + 80*x^5 + 496*x^6 +3648*x^7 +30704*x^8 +...
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PROG
| (PARI) {a(n)=local(A=x); if(n<1, 0, for(i=1, n, A=serreverse(x/sqrt(1+4*A +x*O(x^n)))); polcoeff(A, n))}
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CROSSREFS
| Cf. A087949.
Sequence in context: A109570 A156626 A088501 * A052809 A136631 A002435
Adjacent sequences: A140089 A140090 A140091 * A140093 A140094 A140095
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 15 2008
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