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 A261992 Expansion of psi(x) * f(-x^18)^3 / (phi(-x^3) * f(-x^3)^3) in powers of x where phi(), psi(), f() are Ramanujan theta functions. 2
 1, 1, 0, 6, 5, 0, 25, 19, 0, 84, 61, 0, 248, 174, 0, 666, 455, 0, 1662, 1112, 0, 3912, 2573, 0, 8774, 5689, 0, 18894, 12102, 0, 39289, 24900, 0, 79248, 49759, 0, 155612, 96902, 0, 298338, 184408, 0, 559812, 343722, 0, 1030224, 628717, 0, 1862647, 1130418, 0 (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..1000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^-2 * eta(q^2)^2 * eta(q^6) * eta(q^18)^3 / (eta(q) * eta(q^3)^5) in powers of q. 3 * a(n) = A139214(2*n + 4). a(3*n) = A233698(n). a(3*n + 1) = A128638(n+1). a(3*n + 2) = 0. EXAMPLE G.f. = 1 + x + 6*x^3 + 5*x^4 + 25*x^6 + 19*x^7 + 84*x^9 + 61*x^10 + ... G.f. = q^2 + q^3 + 6*q^5 + 5*q^6 + 25*q^8 + 19*q^9 + 84*q^11 + 61*q^12 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (1/2) x^(-1/8) EllipticTheta[ 2, 0, x^(1/2)] QPochhammer[ x^18]^3 / (EllipticTheta[ 4, 0, x^3] QPochhammer[ x^3]^3), {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^6 + A) * eta(x^18 + A)^3 / (eta(x + A) * eta(x^3 + A)^5), n))}; CROSSREFS Cf. A128638, A139214, A233698. Sequence in context: A193355 A248922 A316253 * A278760 A199724 A126743 Adjacent sequences:  A261989 A261990 A261991 * A261993 A261994 A261995 KEYWORD nonn AUTHOR Michael Somos, Sep 07 2015 STATUS approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)