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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A248395 q-Expansion of the modular form of weight 3/2, g*theta(4) in Tunnell's notation (see Comments). 14
 0, 1, 0, 0, 0, 2, 0, 0, 0, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 4, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS g = Product_{m>=1} ((1-q^(8*m))*(1-q^(16*m)), theta(t) = Sum_{n=-oo..oo} (q^(t*n^2)). Although the OEIS does not normally include sequences in which only every fourth term is nonzero, this one is important enough to warrant an exception. LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math., 72 (1983), 323-334. FORMULA From G. C. Greubel, Jul 02 2018: (Start) Expansion of eta(q^8)*eta(q^16)*theta_{3}(0, q^4)/q in powers of q. Expansion of eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)). (End) MAPLE # This produces a list of the first 100 terms: g:=q*mul((1-q^(8*m))*(1-q^(16*m)), m=1..30); g:=series(g, q, 100); th:=t->series( add(q^(t*n^2), n=-50..50), q, 100); series(g*th(4), q, 100); seriestolist(%); MATHEMATICA QP := QPochhammer; a:= CoefficientList[Series[QP[q^8]*QP[q^16]* EllipticTheta[3, 0, q^4], {q, 0, 60}], q]; Join[{0}, Table[a[[n]], {n, 1, 50}]] (* G. C. Greubel, Jul 02 2018 *) PROG (PARI) q='q+O('q^50); A = eta(q^8)^6/(q*eta(q^4)^2*eta(q^16)); concat([0], Vec(A)) \\ G. C. Greubel, Jul 02 2018 CROSSREFS The nonzero quadrisection is A080966, which has further information and references. Cf. A248394. Used in A248397-A248406. Sequence in context: A328891 A101436 A056170 * A059483 A067618 A279255 Adjacent sequences:  A248392 A248393 A248394 * A248396 A248397 A248398 KEYWORD sign AUTHOR N. J. A. Sloane, Oct 18 2014 STATUS approved

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.

Last modified July 24 18:34 EDT 2021. Contains 346273 sequences. (Running on oeis4.)