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A185699
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Expansion of (11 * E_2(x^11) - E_2(x)) / 2 in powers of x where E_2() is an Eisenstein series.
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2
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5, 12, 36, 48, 84, 72, 144, 96, 180, 156, 216, 12, 336, 168, 288, 288, 372, 216, 468, 240, 504, 384, 36, 288, 720, 372, 504, 480, 672, 360, 864, 384, 756, 48, 648, 576, 1092, 456, 720, 672, 1080, 504, 1152, 528, 84, 936, 864, 576, 1488, 684, 1116, 864, 1176, 648
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OFFSET
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0,1
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COMMENTS
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REFERENCES
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B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 480, Entry 8(i).
Carlos J. Moreno and Samuel S. Wagstaff, Jr., Sums of Squares of Integers, Chapman & Hall/CRC, Boca Raton, London, New York, p. 246 (corrected).
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LINKS
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FORMULA
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Expansion of 5 * (phi(x) * phi(x^11))^2 - 20 * x * (f(x) * f(x^11))^2 + 32 * x^2 * (f(-x^2) * f(-x^22))^2 - 20 * x^3 * (psi(-x) * psi(-x^11))^2 in powers of x where f(), phi(), psi() are Ramanujan theta functions.
Expansion of 5 + 12*Sum_{n>=1} Chi0(n)*n*q^n / (1 - q^n), where Chi0(n) = 1 if gcd(n,11) = 1 and 0 otherwise. See the Moreno-Wagstaff reference p. 246, second equation multiplied by 12 (a misprint has been corrected, after mail exchange with C. J. Moreno). - Wolfdieter Lang, Jan 02 2017
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EXAMPLE
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G.f. = 5 + 12*x + 36*x^2 + 48*x^3 + 84*x^4 + 72*x^5 + 144*x^6 + 96*x^7 + ...
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MATHEMATICA
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terms = 54;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
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PROG
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(PARI) {a(n) = if( n<1, 5 * (n==0), 12 * (sigma( n) - if( n%11, 0, 11 * sigma( n / 11))))};
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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