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 A132212 Expansion of f(-x, -x^7) / f(-x, -x) in powers of q where f(, ) is Ramanujan's general theta function. 1
 1, 1, 2, 4, 6, 10, 16, 23, 34, 50, 71, 100, 140, 192, 262, 356, 476, 634, 840, 1102, 1440, 1872, 2417, 3108, 3980, 5070, 6434, 8135, 10242, 12852, 16076, 20036, 24898, 30852, 38112, 46958, 57708, 70730, 86486, 105508, 128412, 155952, 189004, 228580 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Euler transform of period 8 sequence [ 1, 1, 2, 1, 2, 1, 1, 0, ...]. EXAMPLE G.f. = 1 + x + 2*x^2 + 4*x^3 + 6*x^4 + 10*x^5 + 16*x^6 + 23*x^7 + 34*x^8 + 50*x^9 + ... G.f. = q^9 + q^25 + 2*q^41 + 4*q^57 + 6*q^73 + 10*q^89 + 16*q^105 + 23*q^121 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ Product[ (1 - x^k)^-{ 1, 1, 2, 1, 2, 1, 1, 0}[[Mod[k, 8, 1]]], {k, n}], {x, 0, n}]; (* Michael Somos, Nov 01 2015 *) a[ n_] := SeriesCoefficient[ QPochhammer[ x, x^8] QPochhammer[ x^7, x^8] QPochhammer[ x^8] / EllipticTheta[ 4, 0, x], {x, 0, n}]; (* Michael Somos, Nov 01 2015 *) PROG (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, n, (1 - x^k + x*O(x^n))^-[ 0, 1, 1, 2, 1, 2, 1, 1][k%8 + 1]), n))}; CROSSREFS Sequence in context: A076529 A323283 A279715 * A241903 A261204 A293422 Adjacent sequences:  A132209 A132210 A132211 * A132213 A132214 A132215 KEYWORD nonn AUTHOR Michael Somos, Aug 13 2007 STATUS approved

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Last modified June 19 23:01 EDT 2019. Contains 324222 sequences. (Running on oeis4.)