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 A260676 Expansion of phi(x) * psi(x^30) in powers of x where phi(), chi() are Ramanujan theta functions. 2
 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0 (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..5000 Michael Somos, Introduction to Ramanujan theta functions Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-15/4) * eta(q^2)^5 * eta(q^60)^2 / (eta(q)^2 * eta(q^4)^2 * eta(q^30)) in powers of q. Euler transform of a period 60 sequence. 2 * a(n) = A260671(4*n + 15). EXAMPLE G.f. = 1 + 2*x + 2*x^4 + 2*x^9 + 2*x^16 + 2*x^25 + x^30 + 2*x^31 + 2*x^34 + ... G.f. = q^15 + 2*q^19 + 2*q^31 + 2*q^51 + 2*q^79 + 2*q^115 + q^135 + 2*q^139 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[3, 0, x] QPochhammer[x^60]^2 / QPochhammer[x^30], {x, 0, n}]; PROG (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^60 + A)^2 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^30 + A)), n))}; (Magma) m:=130; f:= func< q | (&*[( (1-q^(2*n))^5*(1-q^(60*n))^2 )/( (1-q^n)^2*(1-q^(4*n))^2*(1-q^(30*n)) ): n in [1..m+1]]) >; R:=PowerSeriesRing(Integers(), m); Coefficients(R!( f(x) )); // G. C. Greubel, Feb 02 2023 (SageMath) m = 130 def f(q): return product( ((1-q^(2*n))^5*(1-q^(60*n))^2)/((1-q^n)^2*(1-q^(4*n))^2*(1-q^(30*n))) for n in range(1, m+2)) def A260676_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( f(x) ).list() A260676_list(m) # G. C. Greubel, Feb 02 2023 CROSSREFS Cf. A260671. Sequence in context: A318985 A033749 A033743 * A033741 A033735 A033731 Adjacent sequences: A260673 A260674 A260675 * A260677 A260678 A260679 KEYWORD nonn AUTHOR Michael Somos, Nov 14 2015 STATUS approved

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Last modified June 21 07:08 EDT 2024. Contains 373540 sequences. (Running on oeis4.)