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 A262175 Expansion of chi(x) * psi(x^6) * phi(-x^30) / (f(-x^4) * psi(x^5)) in powers of x where phi(), psi(), chi(), f() are Ramanujan theta functions. 1
 1, 1, 0, 1, 2, 1, 1, 3, 4, 4, 4, 6, 8, 8, 8, 11, 16, 17, 17, 23, 31, 32, 32, 42, 54, 56, 59, 77, 94, 99, 106, 129, 156, 167, 178, 214, 257, 276, 295, 350, 416, 445, 474, 559, 652, 698, 752, 877, 1012, 1089, 1174, 1349, 1542, 1662, 1792, 2042, 2327, 2512, 2706 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). LINKS Vaclav Kotesovec, 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 Expansion of q^(1/12) * eta(q^2)^2 * eta(q^5) * eta(q^12)^2 * eta(q^30)^2 / (eta(q) * eta(q^4)^2 * eta(q^6) * eta(q^10)^2 * eta(q^60)) in powers of q. Euler transform of a period 60 sequence. a(n) = A139632(3*n). a(n) ~ exp(Pi*sqrt(3*n/10)) / (2^(5/4) * 3^(3/4) * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Nov 16 2017 EXAMPLE G.f. = 1 + x + x^3 + 2*x^4 + x^5 + x^6 + 3*x^7 + 4*x^8 + 4*x^9 + ... G.f. = q^-1 + q^11 + q^35 + 2*q^47 + q^59 + q^71 + 3*q^83 + 4*q^95 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ x^(-1/8) QPochhammer[ -x, x^2] EllipticTheta[ 2, 0, x^3] EllipticTheta[ 4, 0, x^30] / (QPochhammer[ x^4] EllipticTheta[ 2, 0, x^(5/2)]), {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^5 + A) * eta(x^12 + A)^2 * eta(x^30 + A)^2 / (eta(x + A) * eta(x^4 + A)^2 * eta(x^6 + A) * eta(x^10 + A)^2 * eta(x^60 + A)), n))}; CROSSREFS Cf. A139632. Sequence in context: A302097 A307277 A210691 * A278028 A124424 A057044 Adjacent sequences:  A262172 A262173 A262174 * A262176 A262177 A262178 KEYWORD nonn AUTHOR Michael Somos, Sep 13 2015 STATUS approved

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Last modified April 19 07:31 EDT 2021. Contains 343109 sequences. (Running on oeis4.)