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 A280384 Expansion of f(x)^3 * f(-x^2) * chi(x^3)^3 in powers of x where chi(), f() are Ramanujan theta functions. 3
 1, 3, -1, -5, 8, -1, -28, 11, 10, -41, 41, 26, -53, 84, 21, -101, 76, 3, -129, 99, 14, -190, 187, 59, -299, 263, 62, -336, 340, 27, -459, 370, 111, -645, 518, 228, -774, 806, 179, -973, 882, 147, -1233, 955, 291, -1565, 1325, 395, -1883, 1767, 338, -2318, 1994 (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). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Amanda Clemm, Modular Forms and Weierstrass Mock Modular Forms, Mathematics, volume 4, issue 1, (2016) Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q * eta(q^12)^10 * eta(q^36)^6 / (eta(q^6)^3 * eta(q^18)^3 * eta(q^24)^3 * eta(q^72)^3) in powers of q^6. Euler transform of period 12 sequence [3, -7, 6, -4, 3, -10, 3, -4, 6, -7, 3, -4, ...]. a(n) = (-1)^n * A280328(n). a(5*n + 1) / a(1) == A187076(n) (mod 5). a(125*n + 21) / a(21) == A187076(n) (mod 25). EXAMPLE G.f. = 1 + 3*x - x^2 - 5*x^3 + 8*x^4 - x^5 - 28*x^6 + 11*x^7 + 10*x^8 + ... G.f. = q^-1 + 3*q^5 - q^11 - 5*q^17 + 8*q^23 - q^29 - 28*q^35 + 11*q^41 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x]^3 QPochhammer[ x^2] QPochhammer[ -x^3, 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)^10 * eta(x^6 + A)^6 / (eta(x + A)^3 * eta(x^3 + A)^3 * eta(x^4 + A)^3 * eta(x^12 + A)^3), n))}; CROSSREFS Cf. A187076, A280328. Sequence in context: A209831 A284367 A280328 * A124420 A176105 A094353 Adjacent sequences:  A280381 A280382 A280383 * A280385 A280386 A280387 KEYWORD sign AUTHOR Michael Somos, Jan 01 2017 STATUS approved

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Last modified July 24 21:47 EDT 2021. Contains 346273 sequences. (Running on oeis4.)