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 A260675 Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions. 2
 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,16 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-1/4) * eta(q^4)^2 * eta(q^30)^5 / (eta(q^2) * eta(q^15)^2 * eta(q^60)^2) in powers of q. Euler transform of a period 60 sequence. 2 * a(n) = A260671(4*n + 1). EXAMPLE G.f. = 1 + x^2 + x^6 + x^12 + 2*x^15 + 2*x^17 + x^20 + 2*x^21 + 2*x^27 + ... G.f. = q + q^9 + q^25 + q^49 + 2*q^61 + 2*q^69 + q^81 + 2*q^85 + 2*q^109 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (1/2) x^(-1/4) EllipticTheta[ 2, 0, x] EllipticTheta[ 3, 0, x^15], {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^2 * eta(x^30 + A)^5 / (eta(x^2 + A) * eta(x^15 + A)^2 * eta(x^60 + A)^2), n))}; CROSSREFS Cf. A260671. Sequence in context: A254886 A030219 A287345 * A035147 A101673 A091395 Adjacent sequences:  A260672 A260673 A260674 * A260676 A260677 A260678 KEYWORD nonn AUTHOR Michael Somos, Nov 14 2015 STATUS approved

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Last modified April 13 06:02 EDT 2021. Contains 342935 sequences. (Running on oeis4.)