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 A260600 Expansion of x * psi(x^3) * psi(x^12) / f(-x) in powers of x where psi(), f() are Ramanujan theta functions. 1
 0, 1, 1, 2, 4, 6, 9, 14, 20, 29, 42, 58, 80, 111, 149, 200, 268, 353, 463, 606, 784, 1011, 1299, 1656, 2104, 2664, 3354, 4208, 5264, 6555, 8138, 10076, 12428, 15288, 18758, 22944, 27996, 34081, 41377, 50124, 60592, 73075, 87951, 105652, 126652, 151547, 181015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], 2015-2016. Eric Weisstein's World of Mathematics, Ramanujan Theta Functions FORMULA Expansion of q^(-5/6) * eta(q^6)^2 * eta(q^24)^2 / (eta(q) * eta(q^3) * eta(q^12)) in powers of q. Euler transform of period 24 sequence [1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, -1, ...]. -2 * a(n) = A260574(4*n + 3). a(n) ~ exp(sqrt(2*n/3)*Pi) / (24*sqrt(2*n)). - Vaclav Kotesovec, Oct 14 2015 EXAMPLE G.f. = x + x^2 + 2*x^3 + 4*x^4 + 6*x^5 + 9*x^6 + 14*x^7 + 20*x^8 + ... G.f. = q^11 + q^17 + 2*q^23 + 4*q^29 + 6*q^35 + 9*q^41 + 14*q^47 + ... MATHEMATICA a[ n_] := SeriesCoefficient[ EllipticTheta[ 2, 0, x^(3/2)] EllipticTheta[ 2, 0, x^6] / ( 4 x^(7/8) QPochhammer[ x]), {x, 0, n}]; nmax=60; CoefficientList[Series[x*Product[(1-x^(6*k)) * (1-x^(24*k)) * (1+x^(3*k)) * (1+x^(12*k)) / ((1-x^k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 14 2015 *) PROG (PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^6 + A)^2 * eta(x^24 + A)^2 / (eta(x + A) * eta(x^3 + A) * eta(x^12 + A)), n))}; (PARI) q='q+O('q^99); concat(0, Vec(eta(q^6)^2*eta(q^24)^2 / (eta(q)*eta(q^3)*eta(q^12)))) \\ Altug Alkan, Mar 18 2018 CROSSREFS Cf. A260574. Sequence in context: A295341 A139135 A097197 * A119737 A038718 A042942 Adjacent sequences:  A260597 A260598 A260599 * A260601 A260602 A260603 KEYWORD nonn AUTHOR Michael Somos, Jul 29 2015 STATUS approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)