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Search: id:A050203
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| A050203 |
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a(n) is the coefficient of the term a^(-n) in the asymptotic series for the least positive zero of the generalized Rogers-Ramanujan continued fraction. |
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+0
1
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| 1, -1, 2, -6, 21, -79, 311, -1266, 5289, -22553, 97763, -429527, 1908452, -8560532, 38713510, -176318081, 808018789, -3723242051, 17239848937, -80174546765, 374319144257, -1753833845882, 8243964424236, -38865436663306
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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Berndt, B. C.; Huang, S.-S.; Sohn, J.; and Son, S. H. "Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook."
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LINKS
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Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction
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PROGRAM
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(PARI) {RR(n, w, z, p, po, i, m, h, h1, j, w1, h2)=w=1+O(x^(n+1)); p=1; po =1; for(i=1, n, w=p-po*x*q^i; po=p; p=w); m=poldegree(w); w1=0; for(i=0, m, h=polcoeff(w, i); h1=0; for (j=1, n-1+i, h1=h1+polcoeff(h, j)*q^j); w1=w1+h1*x^i); q=0; for (i=1, n-1, q=q+s[i]/x^i); q=q+y/x^n; z=eval(w1); kill(q); h2=polcoeff(z, -(n-1)); polcoeff(h2, 1)*polcoeff(h2, 0)*(-1)} s=vector(30); s[1]=1; print(s[1]); for (j=2, 30, s[j]=RR(j); print(s[j]));
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CROSSREFS
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Adjacent sequences: A050200 A050201 A050202 this_sequence A050204 A050205 A050206
Sequence in context: A026737 A111279 A033321 this_sequence A112806 A106223 A106228
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KEYWORD
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sign
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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EXTENSIONS
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PARI program and more terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 13 2000
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