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 A262090 Expansion of f(x^3, x^21) / f(-x^2, -x^4) where f(, ) is the Ramanujan general theta function. 2
 1, 0, 1, 1, 2, 1, 3, 2, 5, 3, 7, 5, 11, 7, 15, 11, 22, 15, 30, 22, 42, 31, 56, 43, 77, 58, 101, 80, 135, 106, 177, 142, 232, 187, 299, 246, 388, 319, 495, 415, 634, 532, 803, 683, 1017, 869, 1277, 1103, 1605, 1390, 2000, 1751, 2492, 2189, 3087, 2733, 3819 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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..2500 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Euler transform of period 48 sequence [ 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, ...]. a(n) = - A143067(2*n + 3). EXAMPLE G.f. = 1 + x^2 + x^3 + 2*x^4 + x^5 + 3*x^6 + 2*x^7 + 5*x^8 + 3*x^9 + ... G.f. = q^77 + q^173 + q^221 + 2*q^269 + q^317 + 3*q^365 + 2*q^413 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ QPochhammer[ -x^3, x^24] QPochhammer[ -x^21, x^24] QPochhammer[ x^24] / QPochhammer[ x^2], {x, 0, n}]; PROG (PARI) {a(n) = if( n<0, 0, A = x * O(x^n); polcoeff( subst( prod(k=1, n\3, 1 - x^k * [1, 1, 0, 0, 0, 0, 0, 1][k%8 + 1], 1 + x * O(x^(n\3))), x, -x^3) / eta(x^2 + x * O(x^n)), n))}; CROSSREFS Cf. A143067. Sequence in context: A008731 A114209 A132091 * A239881 A051792 A053602 Adjacent sequences:  A262087 A262088 A262089 * A262091 A262092 A262093 KEYWORD nonn AUTHOR Michael Somos, Sep 10 2015 STATUS approved

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Last modified May 17 12:38 EDT 2022. Contains 353746 sequences. (Running on oeis4.)