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Search: id:A116603
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| 1, 2, -1, 4, -21, 138, -1091, 10088, -106918, 1279220, -17070418, 251560472, -4059954946, 71250808916, -1351381762990, 27552372478592, -601021307680207, 13969016314470386, -344653640328891233, 8997206549370634644
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant, J. Math. Anal. Appl. (to appear).
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LINKS
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Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant
Eric Weisstein's World of Mathematics, Goebels Sequence
J. Sondow and P. Hadjicostas, The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant
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FORMULA
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G.f. A(x) satisfies (1+x)^2=A(x)^2/A(x/(1+x)).
A003504(n) ~ C^(2^n)(n+2-1/n+4/n^2-21/n^3+138/n^4-1091/n^5+...) where C=1.04783144757... (see A115632).
A052129(n) ~ s^(2^n)/(n+2-1/n+4/n^2-21/n^3+138/n^4-1091/n^5+...) where s=1.661687949633... (see A112302).
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=1; for(k=1, n, A=truncate(A+O(x^k))+x*O(x^k); A=-A+2/subst(A^(-1/2), x, x/(1+x))*(1+x); ); polcoeff(A, n))}
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CROSSREFS
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Cf. A052129, A112302, A123851, A123852, A123853, A123854.
Sequence in context: A010252 A032105 A053565 this_sequence A158356 A015939 A061655
Adjacent sequences: A116600 A116601 A116602 this_sequence A116604 A116605 A116606
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 18 2006
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