OFFSET
1,2
REFERENCES
R. A. Rankin, The zeros of Eisenstein series, Publ. Ramanujan Institute 1 (1969), 137-144. (On page 139).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..300
Oscar E. González, An observation of Rankin on Hankel determinants, Department of Mathematics, University of Illinois at Urbana-Champaign, 2018.
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, AMS/IP Studies in Advanced Mathematics, vol. 7, 97--126, (1998). See esp. p. 110.
FORMULA
a(n) ~ Pi^(3/2) * 1728^n / (72 * Gamma(1/4)^4 * sqrt(3*n)). - Vaclav Kotesovec, Apr 07 2018
MATHEMATICA
nmax = 20; E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, nmax + 1}] + O[x]^(nmax + 1); E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, nmax + 1}] + O[x]^(nmax + 1); E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, nmax + 1}] + O[x]^(nmax + 1); A000521x = Normal[Series[(1728 E4[x]^3/(E4[x]^3 - E6[x]^2)), {x, 0, nmax}]]; expansion = CoefficientList[Series[E2[x]*E4[x]/(E6[x]*(1728 E4[x]^3/(E4[x]^3 - E6[x]^2))), {x, 0, nmax}], x]; A[x_] := Sum[c[k]/A000521x^k, {k, 0, nmax}]; Array[c, nmax] /. Solve[CoefficientList[Series[A[x], {x, 0, nmax}], x] == expansion][[1]] (* Vaclav Kotesovec, Apr 07 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
STATUS
approved