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 A227695 Expansion of psi(x)^2 * phi(-x)^6 in powers of x where phi(), psi() are Ramanujan theta functions. 4
 1, -10, 37, -50, -30, 128, -25, -34, -320, 310, 410, -370, -87, -410, 320, 30, 500, 384, -630, -640, -359, 300, -326, 2560, -110, -1098, -1280, -370, 1490, -1850, 269, 1500, 1216, 640, 570, -3328, 340, -2010, -1110, 1790, 768, 3200, 303, 750, -1600, -442 (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^(-1/4) * (eta(q)^5 / eta(q^2))^2 in powers of q. Expansion of phi(-x)^5 * f(-x^2)^3 = phi(-x)^2 * f(-x)^6 in powers of x where phi(), f() are Ramanujan theta functions. Euler transform of period 2 sequence [ -10, -8, ...]. G.f. is a period 1 Fourier series which satisfies f(-1 / (32 t)) = 8192 (t / i)^4 g(t) where q = exp(2 Pi i t) and g() is the g.f. for A227317. G.f.: (Product_{k>0} (1 - x^k)^5 / (1 - x^(2*k)))^2. Convolution of A000729 and A104794. EXAMPLE G.f. = 1 - 10*x + 37*x^2 - 50*x^3 - 30*x^4 + 128*x^5 - 25*x^6 - 34*x^7 - 320*x^8 + ... G.f. = q - 10*q^5 + 37*q^9 - 50*q^13 - 30*q^17 + 128*q^21 - 25*q^25 - 34*q^29 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ (QPochhammer[ x]^5 / QPochhammer[ x^2])^2, {x, 0, n}]; PROG (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^5 / eta(x^2 + A))^2, n))}; CROSSREFS Cf. A000729, A104794, A227317. Sequence in context: A139242 A139236 A212795 * A247792 A372373 A096000 Adjacent sequences: A227692 A227693 A227694 * A227696 A227697 A227698 KEYWORD sign AUTHOR Michael Somos, Sep 02 2013 STATUS approved

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Last modified May 27 09:39 EDT 2024. Contains 372851 sequences. (Running on oeis4.)