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 A260166 Expansion of phi(x^2) * f(-x^3)^3 / chi(-x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions. 1
 1, 2, 5, 7, 9, 11, 10, 15, 14, 19, 21, 21, 28, 24, 29, 26, 26, 35, 37, 39, 41, 34, 43, 47, 49, 56, 42, 55, 57, 50, 56, 50, 60, 74, 69, 76, 52, 70, 84, 79, 81, 66, 85, 74, 98, 91, 74, 88, 97, 99, 86, 84, 105, 107, 109, 122, 90, 98, 124, 119, 121, 105, 125, 127 (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^(-11/24) * eta(q^3)^3 * eta(q^4)^5 / (eta(q)^2 * eta(q^8)^2) in powers of q. Euler transform of period 24 sequence [ 2, 2, -1, -3, 2, -1, 2, -1, -1, 2, 2, -6, 2, 2, -1, -1, 2, -1, 2, -3, -1, 2, 2, -4, ...]. 3 * a(n) = A260158(4*n + 1). EXAMPLE G.f. = 1 + 2*x + 5*x^2 + 7*x^3 + 9*x^4 + 11*x^5 + 10*x^6 + 15*x^7 + 14*x^8 + ... G.f. = q^11 + 2*q^35 + 5*q^59 + 7*q^83 + 9*q^107 + 11*q^131 + 10*q^155 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 3, 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^3 + A)^3 * eta(x^4 + A)^5 / (eta(x + A)^2 * eta(x^8 + A)^2), n))}; CROSSREFS Cf. A260158. Sequence in context: A174272 A062288 A077059 * A007300 A256699 A247421 Adjacent sequences:  A260163 A260164 A260165 * A260167 A260168 A260169 KEYWORD nonn AUTHOR Michael Somos, Nov 09 2015 STATUS approved

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Last modified June 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)