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A247133 Expansion of f(-x, -x^11) in powers of x where f() is a Ramanujan theta function.

%I A247133 #24 Jul 23 2025 11:33:22
%S A247133 1,-1,0,0,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A247133 0,1,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A247133 0,0,-1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N A247133 Expansion of f(-x, -x^11) in powers of x where f() is a Ramanujan theta function.
%H A247133 Seiichi Manyama, <a href="/A247133/b247133.txt">Table of n, a(n) for n = 0..1000</a>
%H A247133 Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H A247133 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F A247133 Euler transform of period 12 sequence [ -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, ...].
%F A247133 G.f.: Product_{k>0} (1 - x^(12*k)) * (1 - x^(12*k - 1)) * (1 - x^(12*k - 11)).
%F A247133 Convolution inverse of A210964.
%e A247133 G.f. = 1 - x - x^11 + x^14 + x^34 - x^39 - x^69 + x^76 + x^116 - x^125 + ...
%e A247133 G.f. = q^25 - q^49 - q^289 + q^361 + q^841 - q^961 - q^1681 + q^1849 + ...
%o A247133 (PARI) {a(n) = my(m = 24*n + 25); if( issquare(m, &m) && (m%12==5 || m%12==7), (-1)^((m+6) \ 12))};
%Y A247133 Cf. A210964.
%K A247133 sign
%O A247133 0,1
%A A247133 _Michael Somos_, Jan 10 2015