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!)
 A170772 Expansion of ( phi(q) * phi(q^63) + phi(-q) * phi(-q^63) + 4 * q^16 * psi(q^2) * psi(q^126) ) ^ 2 in powers of q^2 where phi(), psi() are Ramanujan theta functions. 4
 4, 0, 16, 0, 16, 0, 0, 0, 32, 16, 64, 48, 0, 32, 16, 0, 96, 64, 48, 64, 96, 0, 80, 48, 0, 64, 128, 64, 16, 80, 0, 96, 144, 0, 128, 0, 112, 96, 128, 0, 224, 160, 0, 128, 240, 96, 208, 160, 0, 0, 304, 0, 256, 112, 192, 224, 32, 0, 240, 128, 0, 192, 224, 16, 336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). REFERENCES Bruce C. Berndt, Ramanujan's Notebooks, Part IV, Springer-Verlag, 1984; see Entry 27, pp. 170-171. This is the right side of (27.1). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions EXAMPLE G.f. = 4 + 16*x^2 + 16*x^4 + 32*x^8 + 16*x^9 + 64*x^10 + 48*x^11 + ... G.f. = 4 + 16*q^4 + 16*q^8 + 32*q^16 + 16*q^18 + 64*q^20 + 48*q^22 + 32*q^26 + 16*q^28 + ... MATHEMATICA QP = QPochhammer; f[q_] := QPochhammer[-q, -q]; p[q_] := EllipticTheta[3, 0, q]; u[q_] := (1/2)*q^(-1/8)*EllipticTheta[2, 0, Sqrt[q]]; a[n_] := SeriesCoefficient[(p[q]*p[q^63] + p[-q]*p[-q^63] + 4*q^16*u[q^2]*u[q^(126)])^2, {q, 0, n}]; Table[a[n], {n, 0, 100}][[ ;; ;; 2]] (* G. C. Greubel, Dec 05 2017 *) CROSSREFS Cf. A170770, A170771, A170773. Sequence in context: A060052 A059065 A170771 * A079986 A134746 A210067 Adjacent sequences:  A170769 A170770 A170771 * A170773 A170774 A170775 KEYWORD nonn AUTHOR Michael Somos, Dec 10 2009 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 May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)