A105097 Expansion of Delta(tau)/E_4(tau)^2.

1, -504, 180252, -56364992, 16415391870, -4574618335008, 1237162549543256, -327377686829760000, 85212608926827807477, -21894492009015306942480, 5567179862617316105012532, -1403483985988949037403977984

Offset: 1

Author

N. J. A. Sloane, Apr 07 2005

Keywords

• sign
• easy

Comments

According to Paşol and Zudilin, a(n) is divisible by n. - F. Chapoton, Aug 10 2021

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..423
• Richard E. Borcherds, Automorphic forms with singularities on Grassmannians, arXiv:alg-geom/9609022, 1996-1997; Invent. Math. 132 (1998), 491-562.
• Vicenţiu Paşol and Wadim Zudilin, Magnetic (quasi-)modular forms, arXiv:2009.14609 [math.NT], 2020.

Crossrefs

Cf. A000594, A004009, A008410.

Programs

PARI

{a(n)=if(n<1,0,polcoeff( x*eta(x+x*O(x^n))^24/sum(k=1,n,480*sigma(k,7)*x^k,1),n))} /* Michael Somos, Apr 07 2005 */

Formula

a(n) ~ -(-1)^n * exp(Pi*sqrt(3)*n) * n / 192. - Vaclav Kotesovec, Jun 07 2018

Extensions

More terms from Michael Somos, Apr 07 2005