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 A257651 Expansion of chi(x)^2 * f(-x^6)^3 in powers of x where chi(), f() are Ramanujan theta functions. 2
 1, 2, 1, 2, 4, 4, 2, 0, 6, 6, 1, 4, 6, 8, 2, 0, 7, 6, 4, 6, 8, 8, 4, 0, 10, 8, 2, 6, 10, 12, 0, 0, 9, 14, 6, 6, 12, 8, 6, 0, 10, 12, 1, 10, 14, 8, 4, 0, 16, 14, 6, 8, 8, 16, 8, 0, 12, 14, 2, 10, 12, 16, 0, 0, 20, 10, 7, 8, 20, 20, 6, 0, 10, 16, 4, 10, 20, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700). Cubic AGM theta functions: a(q) (see A004016), b(q) (A005928), c(q) (A005882). LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of phi(x^3) * f(x, x^5)^2 in powers of x where phi(), f() are Ramanujan theta functions. Expansion of phi(x) * c(x^2) / 3 in powers of x where phi() is a Ramanujan theta function and c() is a cubic AGM theta function. Expansion of q^(-2/3) * eta(q^2)^4 * eta(q^6)^3 / (eta(q)^2 * eta(q^4)^2) in powers of q. Euler transform of period 12 sequence [ 2, -2, 2, 0, 2, -5, 2, 0, 2, -2, 2, -3, ...]. a(n) = a(4*n + 2) = A213592(2*n + 1). a(2*n) = A213592(n). a(2*n + 1) = 2 * A213607(n). a(8*n + 2) = A213592(n). a(8*n + 3) = 2 * A213617(n). a(8*n + 5) = 4 * A213023(n). a(8*n + 6) = 2 * A213607(n). a(8*n + 7) = 0. EXAMPLE G.f. = 1 + 2*x + x^2 + 2*x^3 + 4*x^4 + 4*x^5 + 2*x^6 + 6*x^8 + 6*x^9 + ... G.f. = q^2 + 2*q^5 + q^8 + 2*q^11 + 4*q^14 + 4*q^17 + 2*q^20 + 6*q^26 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x, x^2]^2 QPochhammer[ x^6]^3, {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^4 * eta(x^6 + A)^3 / (eta(x + A)^2 * eta(x^4 + A)^2), n))}; CROSSREFS Cf. A213023, A213592, A213607, A213617. Sequence in context: A105022 A263293 A230535 * A275122 A264569 A265601 Adjacent sequences:  A257648 A257649 A257650 * A257652 A257653 A257654 KEYWORD nonn AUTHOR Michael Somos, Jul 25 2015 STATUS approved

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Last modified January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)