A305494 - OEIS

%I #25 Jun 03 2018 07:43:53

%S 0,1728,-3375,8000,-32768,54000,-191025,287496,-884736,1264000,

%T -3491750,4834944,-12288000,16581375,-39491307,52250000,-117964800,

%U 153542016,-331531596,425692800,-884736000,1122662608,-2257834125,2835810000,-5541101568,6896880000,-13136684625

%N Let s(D) = Sum_{(a,b,c)} j((-b+sqrt(D))/(2*a)) where (a,b,c) is taken over all the primitive reduced binary quadratic forms a*x^2+b*xy+c*y^2 with b^2-4*ac = D. This sequence is s(D) as D runs through the numbers -3, -4, -7, -8, -11, -12, ... .

%H Seiichi Manyama, <a href="/A305494/b305494.txt">Table of n, a(n) for n = 1..1000</a>

%e In the case D = -15,

%e j((1+sqrt(-15))/2) + j((1+sqrt(-15))/4) = (-191025-85995*sqrt(5))/2 + (-191025+85995*sqrt(5))/2 = -191025.

%e   ----+-------------------------------------------+---------

%e     D | Coefficients of Hilbert class polynomial  |   a(n)

%e   ----+-------------------------------------------+---------

%e    -3 |              0,            1;             |        0

%e    -4 |          -1728,            1;             |     1728

%e    -7 |           3375,            1;             |    -3375

%e    -8 |          -8000,            1;             |     8000

%e   -11 |          32768,            1;             |   -32768

%e   -12 |         -54000,            1;             |    54000

%e   -15 |     -121287375,       191025,        1;   |  -191025

%e   -16 |        -287496,            1;             |   287496

%e   -19 |         884736,            1;             |  -884736

%e   -20 |     -681472000,     -1264000,        1;   |  1264000

%e   -23 | 12771880859375,  -5151296875,  3491750, 1;| -3491750

%e   -24 |    14670139392,     -4834944,        1;   |  4834944

%Y Cf. A014601, A032354, A305474.

%K sign

%O 1,2

%A _Seiichi Manyama_, Jun 02 2018