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 A224825 Expansion of psi(x) * psi(x^3)^2 in powers of x where psi() is a Ramanujan theta function. 2
 1, 1, 0, 3, 2, 0, 4, 1, 0, 5, 3, 0, 5, 4, 0, 5, 1, 0, 7, 5, 0, 7, 4, 0, 9, 0, 0, 7, 6, 0, 6, 6, 0, 11, 3, 0, 8, 5, 0, 10, 6, 0, 8, 2, 0, 9, 6, 0, 14, 8, 0, 10, 0, 0, 15, 7, 0, 7, 8, 0, 7, 4, 0, 14, 9, 0, 14, 6, 0, 16, 1, 0, 8, 11, 0, 13, 10, 0, 13, 0, 0, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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^(-7/8) * eta(q^2)^2 * eta(q^6)^4 / (eta(q) * eta(q^3)^2) in powers of q. Euler transform of period 6 sequence [1, -1, 3, -1, 1, -3, ...]. G.f.: (Sum_{k>0} x^(k*(k-1)/2)) * (Sum_{k>0} x^(3 * k*(k-1)/2))^2. a(3*n + 2) = 0. a(n) = A033768(3*n + 1). a(3*n + 1) = A224823(n). EXAMPLE G.f. = 1 + x + 3*x^3 + 2*x^4 + 4*x^6 + x^7 + 5*x^9 + 3*x^10 + 5*x^12 + 4*x^13 + ... G.f. = q^7 + q^15 + 3*q^31 + 2*q^39 + 4*q^55 + q^63 + 5*q^79 + 3*q^87 + 5*q^103 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, q^(1/2)] EllipticTheta[ 2, 0, q^(3/2)]^2 / (8 q^(7/8)), {q, 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^6 + A)^4 / (eta(x + A) * eta(x^3 + A)^2), n))}; CROSSREFS Cf. A033768, A224823. Sequence in context: A005874 A275622 A129239 * A341413 A290794 A328178 Adjacent sequences: A224822 A224823 A224824 * A224826 A224827 A224828 KEYWORD nonn AUTHOR Michael Somos, Jul 20 2013 STATUS approved

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Last modified September 25 05:35 EDT 2023. Contains 365582 sequences. (Running on oeis4.)