OFFSET
-1,2
REFERENCES
J. M. Borwein and P. B. Borwein, Pi and the AGM, Wiley, 1987, p. 195.
S. Ramanujan, Modular Equations and Approximations to pi, pp. 23-39 of Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., AMS Chelsea 2000. See page 26.
LINKS
Seiichi Manyama, Table of n, a(n) for n = -1..10000
FORMULA
a(n) ~ exp(2*Pi*sqrt(2*n)) / (2^(3/4)*n^(3/4)). - Vaclav Kotesovec, Apr 01 2017
Expansion of (1 + (64*A)^2)/A, where A = (eta(q^2)/eta(q))^24, in powers of q. - G. C. Greubel, Jun 19 2018
EXAMPLE
G.g. = 1/q - 24 + 4372q + 96256q^2 + 1240002q^3 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= (eta[q^2]/eta[q])^24; a := CoefficientList[Series[q*(1 + (64*A)^2)/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)
PROG
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = prod(k=1, (n+1)\2, 1-x^(2*k-1), 1+x*O(x^n))^24; polcoeff( A + x^2*4096/A, n))};
(PARI) q='q+O('q^50); A = q*(eta(q^2)/eta(q))^24; Vec((1+(64*A)^2)/A) \\ G. C. Greubel, Jun 19 2018
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Apr 25 2005
STATUS
approved