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A205988 Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan's general theta function. 7

%I #27 Mar 12 2021 22:24:46

%S 1,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan's general theta function.

%C Characteristic function of A195162. - _Jason Kimberley_, Nov 15 2012

%H Seiichi Manyama, <a href="/A205988/b205988.txt">Table of n, a(n) for n = 0..10000</a>

%H S. Cooper and M. D. Hirschhorn, <a href="http://dx.doi.org/10.1016/S0012-365X(03)00079-7">Results of Hurwitz type for three squares.</a> Discrete Math. 274 (2004), no. 1-3, 9-24. See E(q).

%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 G.f.: f(x, x^9) = Sum_{k in Z} x^(5*k^2 + 4*k).

%e G.f. = 1 + x + x^9 + x^12 + x^28 + x^33 + x^57 + x^64 + x^96 + x^105 + x^145 + ...

%t CoefficientList[Series[QPochhammer[-q, q^10]* QPochhammer[-q^9, q^10]*QPochhammer[q^10, q^10], {q, 0, 160}], q] (* _G. C. Greubel_, Aug 12 2018 *)

%K nonn,easy

%O 0

%A _N. J. A. Sloane_, Feb 02 2012

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Last modified April 23 10:29 EDT 2024. Contains 371905 sequences. (Running on oeis4.)