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%I #13 Mar 12 2021 22:24:48
%S 1,4,12,29,64,132,258,484,876,1539,2636,4416,7256,11716,18624,29190,
%T 45164,69060,104457,156416,232044,341256,497804,720648,1035792,
%U 1478720,2097612,2957590,4146284,5781120,8018821,11067748,15203904,20791590,28310028,38387556
%N Expansion of phi(-x^3) * psi(-x^3) / phi(-x)^2 in powers of x where phi(), psi() are Ramanujan theta functions
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A260546/b260546.txt">Table of n, a(n) for n = 0..1000</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of q^(-3/8) * eta(q^2)^2 * eta(q^3)^3 * eta(q^12) / (eta(q)^4 * eta(q^6)^2) in powers of q.
%F Euler transform of period 12 sequence [ 4, 2, 1, 2, 4, 1, 4, 2, 1, 2, 4, 0, ...].
%F a(n) = A001935(3*n + 1).
%F a(n) ~ exp(Pi*sqrt(3*n/2)) / (2^(11/4) * 3^(3/4) * n^(3/4)). - _Vaclav Kotesovec_, Nov 15 2017
%e G.f. = 1 + 4*x + 12*x^2 + 29*x^3 + 64*x^4 + 132*x^5 + 258*x^6 + 484*x^7 + ...
%e G.f. = q^3 + 4*q^11 + 12*q^19 + 29*q^27 + 64*q^35 + 132*q^43 + 258*q^51 + ...
%t a[ n_] := SeriesCoefficient[ QPochhammer[ x^3]^3 / (EllipticTheta[ 4, 0, x]^2 EllipticTheta[ 4, 0, x^6]), {x, 0, n}];
%o (PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^2 * eta(x^3 + A)^3 * eta(x^12 + A) / (eta(x + A)^4 * eta(x^6 + A)^2), n))};
%Y Cf. A001935.
%K nonn
%O 0,2
%A _Michael Somos_, Jul 28 2015
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