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A036675
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G.f. satisfies A(x) = 1 + x*A(x)^2*A(x^2).
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0
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1, 1, 2, 6, 18, 59, 198, 690, 2450, 8878, 32632, 121518, 457262, 1736526, 6646340, 25613086, 99298674, 387021728, 1515594560, 5960406102, 23530528512, 93216984177, 370450977206, 1476458287082, 5900150928510, 23635544130948
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. 1/(1-z/(1-z/(1-z/(...)))) where z=x/(1-x^2/(1-x^2)) (continued fraction); more generally g.f. C(x/(1-x^2/(1-x^2))) where C(x) is the g.f. for the Catalan numbers (A000108). [Joerg Arndt, Mar 18 2011]
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MAPLE
| A := 1; f := proc(n) global A; coeff(series( 1+x*(A*subs(x=x^2, A)), x, n+1), x, n); end; for n from 1 to 50 do A := series(A+f(n)*x^n, x, n +1); od: A;
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PROG
| (PARI) a(n)=local(A, m); if(n<0, 0, m=2; A=1+O(x); while(m<=n+1, m*=2; A=2/(1+sqrt(1-4*x*subst(A, x, x^2)))); polcoeff(A, n))
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CROSSREFS
| Sequence in context: A150041 A190790 A150042 * A121320 A148460 A148461
Adjacent sequences: A036672 A036673 A036674 * A036676 A036677 A036678
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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