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3, 4, 12, 0, 15, 12, 12, 0, 24, 12, 24, 0, 15, 16, 36, 0, 24, 24, 12, 0, 48, 12, 36, 0, 27, 24, 36, 0, 24, 36, 36, 0, 48, 12, 48, 0, 24, 28, 48, 0, 51, 36, 24, 0, 72, 24, 24, 0, 24, 36, 84, 0, 48, 36
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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Expansion of q^(-1) * (phi^3(q) - phi^3(-q)) / 4 in powers of q^2 where phi() is a Ramanujan theta function. - Michael Somos, Mar 12 2011
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EXAMPLE
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3 + 4*x + 12*x^2 + 15*x^4 + 12*x^5 + 12*x^6 + 24*x^8 + 12*x^9 + ...
3*q + 4*q^3 + 12*q^5 + 15*q^9 + 12*q^11 + 12*q^13 + 24*q^17 + 12*q^19 + ...
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MATHEMATICA
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A005887[n_]:= SeriesCoefficient[(EllipticTheta[3, 0, q]^3 - EllipticTheta[3, 0, -q]^3)/(2 q), {q, 0, n}]; Table[A005887[n]/2, {n, 0, 50}][[1;; ;; 2]] (* G. C. Greubel, Feb 09 2018 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, n = 2*n + 1; polcoeff( sum( k=1, sqrtint(n), 2 * x^k^2, 1 + x*O(x^n))^3 / 2, n))} /* Michael Somos, Mar 12 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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