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 A260167 Expansion of psi(x^4) * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions. 1
 1, 2, 3, 3, 4, 7, 7, 8, 7, 10, 11, 10, 13, 11, 15, 16, 19, 18, 14, 20, 21, 20, 21, 21, 25, 22, 27, 31, 23, 30, 31, 35, 28, 27, 35, 36, 37, 38, 32, 34, 41, 39, 43, 35, 49, 46, 43, 48, 42, 55, 51, 49, 50, 38, 55, 52, 57, 63, 47, 60, 54, 62, 63, 51, 65, 66, 67 (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 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^(-23/24) * eta(q^2)^2 * eta(q^3)^3 * eta(q^8)^2 / (eta(q)^2 * eta(q^4)) in powers of q. Euler transform of period 24 sequence [ 2, 0, -1, 1, 2, -3, 2, -1, -1, 0, 2, -2, 2, 0, -1, -1, 2, -3, 2, 1, -1, 0, 2, -4, ...]. 6 * a(n) = A260158(4*n + 3). EXAMPLE G.f. = 1 + 2*x + 3*x^2 + 3*x^3 + 4*x^4 + 7*x^5 + 7*x^6 + 8*x^7 + 7*x^8 + ... G.f. = q^23 + 2*q^47 + 3*q^71 + 3*q^95 + 4*q^119 + 7*q^143 + 7*q^167 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (1/2) x^(-1/2) EllipticTheta[ 2, 0, x^2] QPochhammer[ x^3]^3 QPochhammer[ -x, x]^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^3 + A)^3 * eta(x^8 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)), n))}; CROSSREFS Cf. A260158. Sequence in context: A119795 A207618 A119614 * A035540 A114863 A152980 Adjacent sequences:  A260164 A260165 A260166 * A260168 A260169 A260170 KEYWORD nonn AUTHOR Michael Somos, Nov 09 2015 STATUS approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)