A160971 - OEIS

A160971

Numerators of constant terms of Fourier series of meromorphic modular forms E_k/Delta, where E_k is the normalized k th Eisenstein series [cf. Serre reference] and Delta is the normalized unique weight-twelve cusp form for the full modular group (the generating function of Ramanujan's tau function.)

%I #4 Feb 28 2018 08:35:18

%S 264,-480,504,-240,82104,0,103128,1024080,4203864,1863840,5672869224,

%T 15790320,81426730488,41356037952960,185023705021848,3639088741200,

%U 631566517273421638632,3701044943799840,6265985243914780011624

%N Numerators of constant terms of Fourier series of meromorphic modular forms E_k/Delta, where E_k is the normalized k th Eisenstein series [cf. Serre reference] and Delta is the normalized unique weight-twelve cusp form for the full modular group (the generating function of Ramanujan's tau function.)

%D J.-P. Serre, A Course in Arithmetic, Springer-Verlag, 1973, p. 93.

%F For 2 <= k <= 1000 and k != 7, the 2-order of the full constant term of E_k/Delta = 3 + ord_2(k - 7).

%t Table[SeriesCoefficient[(1 - (4 n/BernoulliB[2 n])*x/(1 - x)) / QPochhammer[x]^24, {x, 0, 1}], {n, 2, 20}] // Numerator (* _Jean-François Alcover_, Feb 28 2018 *)

%Y Cf. A000594.

%K easy,frac,sign

%O 2,1

%A Barry Brent (barrybrent(AT)iphouse.com), Jun 01 2009