login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A145155 Coefficients in expansion of Delta'(q). 2

%I

%S 1,-48,756,-5888,24150,-36288,-117208,675840,-1022787,-1159200,

%T 5880732,-4451328,-7510594,5625984,18257400,15794176,-117400878,

%U 49093776,202566980,-142195200,-88609248,-282275136,428795256,510935040,-637480625,360508512,-1978535160

%N Coefficients in expansion of Delta'(q).

%C First derivative of cusp form Delta (see A000594).

%H Seiichi Manyama, <a href="/A145155/b145155.txt">Table of n, a(n) for n = 0..1000</a>

%H M. Kaneko and D. Zagier, <a href="http://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf">Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials</a>, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998

%F a(n) = (n+1) * A000594(n+1). - _Seiichi Manyama_, Feb 03 2017

%e 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 + ...

%p 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);

%Y Cf. A000594.

%K sign

%O 0,2

%A _N. J. A. Sloane_, Feb 28 2009

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 23 02:12 EDT 2021. Contains 345395 sequences. (Running on oeis4.)