A145200 Coefficients of expansion of Phi(tau) = E_2*E_4/(E_6*j).

0, 1, -24, 196812, 38262208, 40310333070, 16012430173152, 10091293275887096, 5000566664612497920, 2783095702986935913957, 1463183098457857467833520, 790439623931093138858233092, 421526637613212526260386954496, 226162012708702132169932739559302, 120998755205524059896241960291393216

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..367

M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

Eric Weisstein's World of Mathematics, Eisenstein Series.

Formula

a(n) ~ 2 * Pi^5 * exp(2*Pi*n) / (27 * Gamma(1/4)^8). - Vaclav Kotesovec, Apr 07 2018

Example

G.f. = q - 24*q^2 + 196812*q^3 + 38262208*q^4 + 40310333070*q^5 + 16012430173152*q^6 + ...

Mathematica

a[ n_] := SeriesCoefficient[ (1 - 24 Sum[ DivisorSigma[ 1, k] x^k, {k, n}]) (1 + 240 Sum[ DivisorSigma[ 3, k] x^k, {k, n}]) / ((1 - 504 Sum[ DivisorSigma[ 5, k] x^k, {k, n}]) KleinInvariantJ[ Log[x] / (2 Pi I)] 1728), {x, 0, n}]; (* Michael Somos, Jan 15 2015 *)

Crossrefs

Cf. A000521 (j), A006352 (E_2), A004009 (E_4), A013973 (E_6), A030185.

Sequence in context: A048057 A305757 A058550 * A007240 A289029 A287964

Adjacent sequences: A145197 A145198 A145199 * A145201 A145202 A145203

Keyword

sign

Author

N. J. A. Sloane, Feb 28 2009

Status

approved