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!)
 A170770 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
 1, 0, 2, 0, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 8, 0, 4, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 square root of the right side of (27.1), divided by 2. 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 FORMULA G.f.: ( phi(q^7) * phi(q^9) + phi(-q^7) * phi(-q^9) + 4 * q^4 * psi(q^14) * psi(q^18) ) / 2 in powers of q^2 where phi(), psi() are Ramanujan theta functions. - Michael Somos, May 24 2018 EXAMPLE G.f. = 1 + 2*x^2 + 4*x^8 + 2*x^9 + 2*x^11 + 2*x^14 + 4*x^18 + 2*x^23 + ... G.f. = 1 + 2*q^4 + 4*q^16 + 2*q^18 + 2*q^22 + 2*q^28 + 4*q^36 + 2*q^46 + 2*q^58 + ... MATHEMATICA QP = QPochhammer; p[q_] := EllipticTheta[3, 0, q]; u[q_] := (1/2)*q^(-1/8)*EllipticTheta[2, 0, Sqrt[q]]; a[n_] := SeriesCoefficient[(1/2)*(p[q]*p[q^63] + p[-q]*p[-q^63] + 4*q^16*u[q^2]*u[q^(126)]), {q, 0, n}]; Table[a[n], {n, 0, 100}][[ ;; ;; 2]] (* G. C. Greubel, Dec 05 2017 *) a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 0, q^7] EllipticTheta[ 3, 0, q^9] + 1/2 EllipticTheta[ 2, 0, q^7] EllipticTheta[ 2, 0, q^9], {q, 0, 2 n}, Assumptions -> q>0]; (* Michael Somos, May 24 2018 *) CROSSREFS Cf. A170771, A170772, A170773. Sequence in context: A005871 A005888 A213902 * A107499 A123298 A189877 Adjacent sequences:  A170767 A170768 A170769 * A170771 A170772 A170773 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 14 16:00 EDT 2021. Contains 343884 sequences. (Running on oeis4.)