A050203 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.

1, -1, 2, -6, 21, -79, 311, -1266, 5289, -22553, 97763, -429527, 1908452, -8560532, 38713510, -176318081, 808018789, -3723242051, 17239848937, -80174546765, 374319144257, -1753833845882, 8243964424236, -38865436663306

Offset

1,3

Links

Table of n, a(n) for n=1..24.

Bruce C. Berndt, Sen-Shan Huang, Jaebum Sohn and Seung Hwan Son, Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook, Transactions of the AMS, 352 (2000), 2157-2177.

Eric Weisstein's World of Mathematics, Rogers-Ramanujan Continued Fraction

Prog

(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])); \\ Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 13 2000

Crossrefs

Sequence in context: A150198 A257562 A033321 * A112806 A150199 A150200

Adjacent sequences: A050200 A050201 A050202 * A050204 A050205 A050206

Keyword

sign

Author

Eric W. Weisstein

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 13 2000

Status

approved