A145155 Coefficients in expansion of Delta'(q).
1, -48, 756, -5888, 24150, -36288, -117208, 675840, -1022787, -1159200, 5880732, -4451328, -7510594, 5625984, 18257400, 15794176, -117400878, 49093776, 202566980, -142195200, -88609248, -282275136, 428795256, 510935040, -637480625, 360508512, -1978535160
Offset: 0
Keywords
Examples
G.f. = 1 - 2*24*q + 3*252*q^2 - 4*1472*q^3 + 5*4830*q^4 - 6*6048*q^5 - 7*16744*q^6 + ...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1000
- Masanobu Kaneko and Don 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
Crossrefs
Cf. A000594.
Programs
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Maple
with(numtheory); E:=proc(k) series(1-(2*k/bernoulli(k))*add( sigma[k-1](n)*q^n, n=1..60),q,61); end; Delta:=series((E(4)^3-E(6)^2)/1728,q,60); diff(%,q);
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Mathematica
a[n_] := (n+1)*RamanujanTau[n+1]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Apr 12 2023 *) -
PARI
a(n) = (n+1) * ramanujantau(n+1); \\ Amiram Eldar, Jan 10 2025
Formula
a(n) = (n+1) * A000594(n+1). - Seiichi Manyama, Feb 03 2017
Comments