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 A246832 Expansion of psi(x) * psi(x^2) * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions. 3
 1, 1, 3, 4, 2, 5, 2, 3, 7, 5, 5, 6, 5, 3, 10, 6, 3, 7, 7, 4, 11, 9, 3, 14, 8, 8, 5, 4, 7, 10, 13, 7, 8, 10, 7, 15, 8, 4, 17, 10, 8, 11, 10, 5, 16, 11, 4, 11, 15, 8, 14, 10, 7, 22, 8, 9, 14, 8, 13, 21, 12, 5, 13, 15, 6, 21, 15, 9, 13, 8, 11, 9, 12, 15, 20, 21 (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). 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 psi(x) * psi(x^2)^3 / psi(x^4) in powers of x where psi() is a Ramanujan theta function. Expansion of q^(-3/8) * eta(q^4)^7 / (eta(q) * eta(q^2) * eta(q^8)^2) in powers of q. Euler transform of period 8 sequence [1, 2, 1, -5, 1, 2, 1, -3, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (64 t)) = 2 (t/i)^(3/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A246816. EXAMPLE G.f. = 1 + x + 3*x^2 + 4*x^3 + 2*x^4 + 5*x^5 + 2*x^6 + 3*x^7 + 7*x^8 + ... G.f. = q^3 + q^11 + 3*q^19 + 4*q^27 + 2*q^35 + 5*q^43 + 2*q^51 + 3*q^59 + ... MATHEMATICA eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(-3/8)* eta[q^4]^7/(eta[q]*eta[q^2]*eta[q^8]^2), {q, 0, 60}], q]]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Aug 05 2018 *) PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^4 + A)^7 / (eta(x + A) * eta(x^2 + A) * eta(x^8 + A)^2), n))}; CROSSREFS Cf. A246816. Sequence in context: A090131 A152833 A139525 * A133570 A117041 A209688 Adjacent sequences:  A246829 A246830 A246831 * A246833 A246834 A246835 KEYWORD nonn AUTHOR Michael Somos, Sep 04 2014 STATUS approved

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Last modified May 13 12:16 EDT 2021. Contains 343839 sequences. (Running on oeis4.)