# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a279320
Showing 1-1 of 1

%I A279320 #17 Feb 16 2025 08:33:37
%S A279320 1,2,4,8,15,26,45,74,119,188,291,442,664,982,1435,2076,2972,4214,5929,
%T A279320 8272,11457,15762,21543,29264,39532,53110,70988,94430,125033,164826,
%U A279320 216388,282940,368552,478326,618621,797376,1024485,1312184,1675657,2133664,2709307
%N A279320 Expansion of chi(-x^4) * psi(x^6) / phi(-x) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
%C A279320 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A279320 G. C. Greubel, <a href="/A279320/b279320.txt">Table of n, a(n) for n = 0..2500</a>
%H A279320 Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015.
%H A279320 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A279320 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A279320 Expansion of f(-x^2, -x^10) * f(-x^8) / f(-x)^2 in powers of x where f(, ) is Ramanujan's general theta function.
%F A279320 Expansion of q^(-11/12) * eta(q^2) * eta(q^8) * eta(q^12)^2 / (eta(q)^2 * eta(q^4) * eta(q^6)) in powers of q.
%F A279320 Euler transform of period 24 sequence [ 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 0, ...].
%F A279320 a(n) ~ exp(sqrt(13*n/3)*Pi/2) * 13^(1/4) / (16*sqrt(2)*3^(3/4)*n^(3/4)). - _Vaclav Kotesovec_, Dec 10 2016
%e A279320 G.f. = 1 + 2*x + 4*x^2 + 8*x^3 + 15*x^4 + 26*x^5 + 45*x^6 + 74*x^7 + ...
%e A279320 G.f. = q^11 + 2*q^23 + 4*q^35 + 8*q^47 + 15*q^59 + 26*q^71 + 45*q^83 + ...
%t A279320 a[ n_] := SeriesCoefficient[ x^(-3/4)/2 QPochhammer[ -x^4, x^4] EllipticTheta[ 2, 0, x^3] / EllipticTheta[ 4, 0, x], {x, 0, n}];
%t A279320 a[ n_] := SeriesCoefficient[ 2^(-3/2)/x EllipticTheta[ 2, Pi/4, x] EllipticTheta[ 2, 0, x^3] / QPochhammer[ x]^2, {x, 0, n}];
%t A279320 nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(4*k)) * (1+x^(6*k)) * (1-x^(12*k)) / (1-x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Dec 10 2016 *)
%o A279320 (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A) * eta(x^8 + A) * eta(x^12 + A)^2 / (eta(x + A)^2 * eta(x^4 + A) * eta(x^6 + A)), n))};
%Y A279320 Cf. A131945.
%K A279320 nonn,changed
%O A279320 0,2
%A A279320 _Michael Somos_, Dec 09 2016

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE