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 A170771 Expansion of 2 * ( phi(q) * phi(q^7) * phi(q^9) * phi(q^63) + phi(-q) * phi(-q^7) * phi(-q^9) * phi(-q^63) + 4 * q^4 * f(-q^6)^2 * f(-q^42)^2 ) in powers of q^2 where phi(), psi(), and f() are Ramanujan theta functions. 3
 4, 0, 16, 0, 16, 0, 0, 0, 32, 16, 32, 16, 0, 0, 16, 0, 64, 32, 16, 32, 0, 0, 48, 16, 0, 0, 96, 0, 16, 16, 0, 32, 48, 0, 64, 0, 80, 32, 32, 0, 128, 64, 0, 64, 208, 32, 112, 32, 0, 0, 240, 0, 160, 48, 128, 96, 32, 0, 144, 32, 0, 96, 96, 16, 208, 64, 0, 64, 288, 0, 32, 48 (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 left 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 + 32*x^10 + 16*x^11 + ... G.f. = 4 + 16*q^4 + 16*q^8 + 32*q^16 + 16*q^18 + 32*q^20 + 16*q^22 + 16*q^28 + 64*q^32 + ... 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[2*(p[q]*p[q^7]*p[q^9]*p[q^63] + p[-q]*p[-q^7]*p[-q^9]*p[-q^63] + 4*q^4*f[-q^6]^2*f[-q^42]^2 ), {q, 0, n}]; Table[a[n], {n, 0, 100}][[ ;; ;; 2]] (* G. C. Greubel, Dec 05 2017 *) CROSSREFS Cf. A170770, A170772, A170773. Sequence in context: A095367 A060052 A059065 * A170772 A079986 A134746 Adjacent sequences:  A170768 A170769 A170770 * A170772 A170773 A170774 KEYWORD nonn AUTHOR Michael Somos, Dec 10 2009 STATUS approved

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Last modified May 10 04:04 EDT 2021. Contains 343748 sequences. (Running on oeis4.)