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 A170773 Expansion of ( 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 + 16 * q^20 * psi(q^2) * psi(q^14) * psi(q^18) * psi(q^126) ) / 2 in powers of q^2 where phi(), psi(), and f() are Ramanujan theta functions. 4
 1, 0, 4, 0, 4, 0, 0, 0, 8, 4, 16, 12, 0, 8, 4, 0, 24, 16, 12, 16, 24, 0, 20, 12, 0, 16, 32, 16, 4, 20, 0, 24, 36, 0, 32, 0, 28, 24, 32, 0, 56, 40, 0, 32, 60, 24, 52, 40, 0, 0, 76, 0, 64, 28, 48, 56, 8, 0, 60, 32, 0, 48, 56, 4, 84, 48, 0, 48, 88, 0, 16, 36, 60, 40, 80, 0 (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). This is the convolution square of A170770. REFERENCES Bruce C. Berndt, Ramanujan's Notebooks, Part IV, Springer-Verlag, 1984; see Entry 27, pp. 170-171. This is the corrected left side of (27.1), divided by 4. 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. = 1 + 4*x^2 + 4*x^4 + 8*x^8 + 4*x^9 + 16*x^10 + 12*x^11 + 8*x^13 + ... G.f. = 1 + 4*q^4 + 4*q^8 + 8*q^16 + 4*q^18 + 16*q^20 + 12*q^22 + 8*q^26 + 4*q^28 + ... MATHEMATICA f[q_] := QPochhammer[-q, -q]; p[q_] := EllipticTheta[3, 0, q]; u[q_] := (1/2)*q^(-1/8)*EllipticTheta[2, 0, Sqrt[q]]; A170773[n_] := SeriesCoefficient[(1/2)*(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 + 16*q^20*u[q^2]*u[q^14]*u[q^18]*u[q^(126)]), {q, 0, n}]; Table[A170773[n], {n, 0, 100}][[ ;; ;; 2]] (* G. C. Greubel, Dec 03 2017 *) CROSSREFS Cf. A170770-A170772. Sequence in context: A066273 A028650 A028634 * A028618 A147986 A147988 Adjacent sequences:  A170770 A170771 A170772 * A170774 A170775 A170776 KEYWORD nonn AUTHOR Michael Somos, Dec 10 2009 STATUS approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)