A015682
Expansion of e.g.f. theta_3^(-3/2).
Original entry on oeis.org
1, -3, 15, -105, 873, -8595, 97335, -1233225, 17298225, -266220675, 4444840575, -79989057225, 1543271585625, -31735822993875, 692766164665575, -15995714865755625, 389241925213766625, -9954282875453791875
Offset: 0
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
-
nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(-3/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)
A015664
Expansion of e.g.f. theta_3^(1/2).
Original entry on oeis.org
1, 1, -1, 3, 9, -15, 135, -2205, 21105, 76545, 694575, -6392925, -56600775, 66891825, -19964169225, 741313447875, 5375639894625, 44667168170625, -2328500019470625, 5663134786183875, -466442955127524375, 11513119609487120625
Offset: 0
sqrt(theta_3) = 1 + q - (1/2)*q^2 + (1/2)*q^3 + (3/8)*q^4 - (1/8)*q^5 + (3/16)*q^6 - (7/16)*q^7 + (67/128)*q^8 + (27/128)*q^9 + ...
- J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
Cf.
A015665,
A015666,
A015667,
A015669,
A015671,
A015672,
A015673,
A015675,
A015676,
A015677,
A015678,
A015679.
-
# get basic theta series in maple
maxd:=201:
# get th2, th3, th4 = Jacobi theta constants out to degree maxd
temp0:=trunc(evalf(sqrt(maxd)))+2:
a:=0: for i from -temp0 to temp0 do a:=a+q^( (i+1/2)^2): od:
th2:=series(a,q,maxd); # A098108
a:=0: for i from -temp0 to temp0 do a:=a+q^(i^2): od:
th3:=series(a,q,maxd); # A000122
th4:=series(subs(q=-q,th3),q,maxd); # A002448
series(sqrt(th3),q,maxd); # this sequence
-
nmax = 25; CoefficientList[Series[EllipticTheta[3, 0, x]^(1/2), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 23 2018 *)
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