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%I #15 Mar 12 2021 22:24:44
%S 1,2,3,6,9,14,22,32,46,66,93,130,180,244,331,444,590,780,1024,1334,
%T 1730,2234,2867,3664,4660,5904,7449,9364,11728,14638,18211,22584,
%U 27927,34436,42342,51924,63523,77512,94364,114624,138920,168012,202786,244270
%N Expansion of q / (chi(-q) * chi(-q^11))^2 in powers of q where chi() is a Ramanujan theta function.
%C Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H G. C. Greubel, <a href="/A123631/b123631.txt">Table of n, a(n) for n = 1..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 Euler transform of period 22 sequence [ 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, ...].
%F G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 - v - u*v*(4 + 4*v).
%F G.f. A(x) satisfies 0 = f(A(x), A(x^3)) where f(u, v) = (u^2 + v^2)^2 - u*v * (1 + 3*(u+v) + 4*u*v)^2.
%F a(n) ~ exp(2*Pi*sqrt(2*n/11)) / (2^(11/4) * 11^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017
%e G.f. = q + 2*q^2 + 3*q^3 + 6*q^4 + 9*q^5 + 14*q^6 + 22*q^7 + 32*q^8 + 46*q^9 + ...
%t a[ n_] := SeriesCoefficient[ q / (QPochhammer[ q, q^2] QPochhammer[ q^11, q^22])^2, {q, 0, n}]; (* _Michael Somos_, Apr 26 2015 *)
%t a[ n_] := SeriesCoefficient[ q / (Product[ 1 - q^k, {k, 1, n, 2}] Product[ 1 - q^k, {k, 11, n, 22}])^2, {q, 0, n}]; (* _Michael Somos_, Apr 26 2015 *)
%t nmax = 60; CoefficientList[Series[Product[((1+x^k)*(1+x^(11*k)))^2, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Sep 08 2017 *)
%o (PARI) {a(n) = my(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^22 + A) / (eta(x + A) * eta(x^11 + A)))^2, n))};
%K nonn
%O 1,2
%A _Michael Somos_, Oct 03 2006
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